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trial function method and exact solutions to the generalized nonlinear Schrdinger equation with time-dependent coefficient

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Chinese Physics B 2013年第10期22卷 182-185页

作者：曹瑞张健 College of Mathematics and Software Science Sichuan Normal University Department of Mathematics Heze University

In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.

关键词： generalized nonlinear SchriSdinger equation exact solution trial function method

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Multiple rogue wave solutions for a modified (2+1)-dimensional nonlinear evolution equation

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NONLINEAR DYNAMICS 2024年第22期112卷 20141-20151页

作者： Ma, Zhimin Chen, Bohan Bi, Quanming Chengdu Univ Technol Engn & Tech Coll Leshan 614000 Peoples R China Southwestern Inst Phys Chengdu 610225 Peoples R China Sichuan Normal Univ Visual Comp & Virtual Real Key Lab Sichuan Prov Chengdu 610068 Peoples R China

This study primarily focuses on the multiple rogue wave solutions with a controllable center of the modified (2+1)-dimensional nonlinear evolution equation,which describes wave phenomena in the *** analyze this (2+1)-dimensional nonlinear evolution equation using the Hirota bilinear transformation and a symbolic computation method to derive their solutions for 1-rogue waves, 2-rogue waves, and 3-rogue waves. These dynamic behaviors are effectively illustrated with images,which aid in understanding the nonlinear phenomena described by the equation,thereby enhancing the comprehension of the associated physical processes.

关键词： trial function method Hirota bilinear transformation Dynamic behavior Symbolic computation method

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Dynamics and optical solitons in polarization-preserving fibers for the cubic-quartic complex Ginzburg-Landau equation with quadratic-cubic law nonlinearity

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RESULTS IN PHYSICS 2023年 51卷

作者： Peng, Chen Li, Zhao Chengdu Univ Coll Comp Sci Chengdu 610106 Peoples R China Sichuan Normal Univ VC & VR Key Lab Sichuan Prov Chengdu 610068 Peoples R China

In this paper, the cubic-quartic complex Ginzburg-Landau (CGL) equation is investigated by using the trial function method. The traveling wave hypothesis is applied to convert the CGL equation to an ordinary differential equation (ODE), which is equivalent to a dynamic system. The qualitative behavior, bifurcation of the phase portraits for this system is studied. Furthermore, the chaotic motions in system involving external periodic perturbation are considered. Some new optical solitons, such as Jacobian elliptic function solutions, for CGL equation with quadratic-cubic law nonlinearity are constructed using the complete discrimination system for polynomial method. Moreover, two-dimensional graphs, three-dimensional, corresponding contour and density plots for some acquired solutions are depicted to carry out the physical properties of optical pulse propagation.

关键词： Complex Ginzburg-Landau equation Bifurcation Solition solutions trial function method

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Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model

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NONLINEAR DYNAMICS 2021年第3期105卷 2539-2548页

作者： Chen, Yu-Qiong Tang, Yu-Hao Manafian, Jalil Rezazadeh, Hadi Osman, M. S. Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316022 Zhejiang Peoples R China Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China Univ Tabriz Fac Math Sci Dept Appl Math Tabriz Iran Lankaran State Univ Nat Sci Fac 50 H Aslanov Str Lankaran Azerbaijan Amol Univ Special Modern Technol Fac Engn Technol Amol Iran Cairo Univ Fac Sci Dept Math Giza 12613 Egypt Umm Alqura Univ Fac Appl Sci Dept Math Mecca 21955 Saudi Arabia

Under investigation in this paper is the Ivancevic option pricing model. Based on trial function method, rogue wave and dark wave solutions are constructed. By means of symbolic computation, these analytical solutions are obtained with the Maple. Perturbation solutions are obtained through direct perturbation method. These results will enrich the existing literature of the Ivancevic option pricing model. Dynamical characteristics for rogue waves and dark waves are exhibited by using three-dimensional plots, curve plots, density plots and contour plots.

关键词： trial function method Tanh expansion method Direct perturbation method Ivancevic option pricing equation

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On novel resonant multi-soliton and wave solutions to the (3+1)-dimensional GSWE equation via three effective approaches

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RESULTS IN PHYSICS 2021年 26卷

作者： Kuo, Chun-Ku Ghanbari, Behzad Air Force Acad Dept Aeronaut & Astronaut Kaohsiung 820 Taiwan Kermanshah Univ Technol Dept Basic Sci Kermanshah Iran

In this paper, the generalized shallow water equation (GSWE) is carefully investigated via three state-of-the-art integration schemes, namely the simplified linear superposition principle, velocity resonance, and the trial function method, respectively. The main aim of this work is twofold. The first one is to check the existence of the resonant multi-soliton solutions to GSWE. The second one is to show the power of the trial function method. The simplified linear superposition principle is used to reveal the fact that there have no resonant multi-soliton solutions to GSWE, which is simultaneously confirmed by the velocity resonance. Then, the trial function method is successfully used to obtain new wave solutions. All the newly found solutions are constructed with their existence criteria, and some of them are represented in 3D figures.

关键词： Simplified linear superposition principle Velocity resonance trial function method Resonant multi-soliton Wave solution

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A new ZK-ILW equation for algebraic gravity solitary waves in finite depth stratified atmosphere and the research of squall lines formation mechanism

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2018年第10期75卷 3589-3603页

作者： Guo, Min Zhang, Yu Wang, Man Chen, Yaodeng Yang, Hongwei Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China Nanjing Univ Informat Sci & Technol Minist Educ Key Lab Meteorol Disaster Nanjing 210044 Jiangsu Peoples R China

The research of algebraic gravity solitary waves is an advanced field which has important practical and theoretical value in physical, oceanography, aerology and etc. By calculation condition and theoretical method limit, previous researches mainly focused on the (1 + 1) dimensional models, and (2 + 1) dimensional models were few considered. In this paper, from the non-static equilibrium equation, a new ZK-ILW equation is derived by using multi-scale analysis and perturbation method in finite depth stratified atmosphere, which is the first time obtained. The model can reduce to ZK-BO model (h -> infinity), and ZK model (h -> 0) and is the generalization of the above two models. In order to further understand the nature of algebraic gravity solitary waves, we get the analytical solution of ZK-ILW equation by using the trial function method and discuss the conservation laws. Furthermore, the fission process of algebraic gravity solitary waves is studied, and we can judge that one of the possible formation mechanism of squall lines is the fission of algebraic gravity solitary waves. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： (2+1) dimensional algebraic gravity solitary waves ZK-ILW equation Finite depth stratified atmosphere trial function method Squall lines

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A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property

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NONLINEAR DYNAMICS 2018年第3期91卷 2019-2032页

作者： Yang, Hong Wei Chen, Xin Guo, Min Chen, Yao Deng Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China Nanjing Univ Informat Sci & Technol Minist Educ Key Lab Meteorol Disaster Nanjing 210044 Jiangsu Peoples R China Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China

The BO equation depicts the evolution of algebraic Rossby solitary waves in ocean and atmosphere. But, despite its overt fame, the BO equation is restricted as a two-dimensional model. On the basis of the great success in the soliton theory, a lot of works have recently been directed to three-dimensional models and investigations of solitary waves properties in three-dimensional systems. In this paper, a new ZK-BO equation for three-dimensional algebraic Rossby solitary waves is derived by employing perturbation expansions and stretching transformations of time and space. By virtue of the trial function method, the exact solution of the ZK-BO equation is presented. By comparing the solution with the solution of two-dimensional algebraic Rossby solitary waves, we can find that the wave length of three-dimensional algebraic Rossby solitary waves is shorter while the wave amplitude is higher. Based on the exact solution of ZK-BO equation, the dissipation effect is studied. The results reveal the influence of dissipation effect on the three-dimensional algebraic solitary waves. Further, after theoretical analysis, the conservation laws of three-dimensional algebraic Rossby solitary waves are discussed and the fission property is studied.

关键词： ZK-BO equation Three-dimensional algebraic Rossby solitary waves trial function method Dissipation effect Fission property

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The Boussinesq-BO equation for algebraic gravity solitary waves in baroclinic atmosphere and the research of squall lines formation mechanism

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DYNAMICS OF ATMOSPHERES AND OCEANS 2017年第Dec.期80卷 29-46页

作者： Guo, Min Chen, Xin Chen, Yaodeng Yang, Hongwei Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China Nanjing Univ Informat Sci & Technol Key Lab Meteorol Disaster Minist Educ Nanjing 210044 Jiangsu Peoples R China

The gravity solitary waves are a kind of waves which are caused by the disturbance of static equilibrium. The nonlinearity concentration of the gravity solitary waves makes the energy assemble together and forms disastrous weather phenomena, such as squall lines. By the calculation condition and theoretical method limit, previous studies tried hard to reduce the variable numbers and discussed the gravity solitary waves in barotropic atmosphere, but the baroclinic problem of atmosphere is inevitable topic. In this paper, from the basic kinetic equations in baroclinic non-static equilibrium atmosphere, by using multi -scale analysis and perturbation method, a new model is derived to describe the algebraic gravity solitary waves, we call it Boussinesq-BO equation. Comparing with the former models, the Boussinesq-BO model can describe the propagation process of waves in two directions and is more suitable for the real atmosphere condition. With the help of the trial function method, an exact solution of Boussinesq-BO equation is obtained and the fission property of algebraic gravity solitary waves is discussed. Finally, we can find that the fission of algebraic gravity solitary waves is also a possible formation mechanism of squall lines. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Algebraic gravity solitary waves Boussinesq-BO equation Baroclinic atmosphere trial function method Squall lines

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Temperature transients in TRISO type fuel

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ANNALS OF NUCLEAR ENERGY 2015年第Feb.期76卷 172-176页

作者： Garcia-Berrocal, A. Montalvo, C. Blazquez, J. Tech Univ Madrid UPM Appl Phys Nat Resources Dept Madrid 28003 Spain CIEMAT Nucl Fiss Div E-28040 Madrid Spain

The High Temperature Gas-cooled Reactor (HTGR), cooled by gas and moderated by graphite, is the predecessor of the Generation IV Very High Temperature Reactor (VHTR). Recently, the South African project of the Pebble-Bed Modular Reactor (PBMR) seems to merge in high temperature, helium cooled and micro-fuel particles called TRISO in pebble-bed. TRISO particles must not exceed 2000 degrees C due to safety requirements. The inner structure of the fuel element is sufficiently complex to know with a certain uncertainty its heat transfer coefficients. It also explains that the in situ heat transfer time can differ from the one obtained in the laboratory. Hence, a mesoscale simplified analytical model (pebble scale) has been developed in this work in order to study temperature transients in operation. Its assigned coefficients have a certain experimental support. The trial function with physical meaning method is used to solve the model equations and the in situ estimation of the coefficients is achieved by means of thermal noise analysis from thermocouple signals. Instead of complex numerical models, the approximate solutions are very simple and enough for safety requirements and surveillance. Both heat transfer time and conductivity are estimated so that the bumup level of a certain element can be monitored. A case study is presented using data obtained from the literature. This result permits selecting the sampling time of the noise signals, and also optimizing an Autoregressive Moving Average (ARMA) (1,1) model according to the solution provided by the simplified model. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： High Temperature-Gas-cooled Reactor TRISO Thermal noise analysis Thermocouple Thermal conductivity trial function method

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New Solutions to Generalized mKdV Equation

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Communications in Theoretical Physics 2004年第1期41卷 25-28页

作者： FUZun-Tao CHENZhe LIUShi-Kuo LIUShi-Da SchoolofPhysics PekingUniversityBeijing100871China SchoolofPhysics PekingUniversityBeijing100871ChinaCorrespondingauthorEmail：fuzt@***

trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and m... 详细信息

关键词： GmKdV equation solitary wave solution trial function method

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