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)-...
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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.
The Hirota bilinear equation with variable coefficients (VCs) serves as a fundamental model for capturing nonlinear wave dynamics in fluids and oceans. Utilizing the Hirota bilinear framework alongside advanced symbol...
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Applying a direct symbolic computation method combined with variable transformations, some new Jacobi elliptic function solutions are obtained to the short-pulse equation in nonlinear optics. When Jacobi elliptic func...
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Applying a direct symbolic computation method combined with variable transformations, some new Jacobi elliptic function solutions are obtained to the short-pulse equation in nonlinear optics. When Jacobi elliptic function modulus m -> 1 or 0, the travelling wave solutions degenerate to two types of solutions, namely, the loop-like soliton solution and the trigonometric function solution.
A particular attention is paid on a generalized nonlinear Boussinesq equation which can be used to describe the wave dynamics in fluids. Via symbolic computation method, analytical N-soliton solutions, three types of ...
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A particular attention is paid on a generalized nonlinear Boussinesq equation which can be used to describe the wave dynamics in fluids. Via symbolic computation method, analytical N-soliton solutions, three types of breather solutions (namely, Kuznetsov-Ma, Akhmediev and generalized breather solutions), and rogue wave solutions are obtained. The extreme points of rogue waves are analyzed in detail. Furthermore, a type of novel X-like soliton is observed.
In this paper, we use the symbolic computation method to prove the famous Mordell inequality conjecture. By eliminating the constraints using the normalized condition, this problem can be transformed into the non-cons...
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ISBN:
(纸本)9789881563958
In this paper, we use the symbolic computation method to prove the famous Mordell inequality conjecture. By eliminating the constraints using the normalized condition, this problem can be transformed into the non-constraints problem. For the case of n = 3, we verified that this inequality is correct by cylindrical algebraic decomposition;meanwhile, for the case of n = 4, we verify the inequality is also valid for many cases by using the successive difference substitution method.
In this paper, we use the symbolic computation method to prove the famous Mordell inequality conjecture. By eliminating the constraints using the normalized condition, this problem can be transformed into the non-cons...
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In this paper, we use the symbolic computation method to prove the famous Mordell inequality conjecture. By eliminating the constraints using the normalized condition, this problem can be transformed into the non-constraints *** the case of n = 3, we verified that this inequality is correct by cylindrical algebraic decomposition;meanwhile, for the case of n = 4, we verify the inequality is also valid for many cases by using the successive difference substitution method.
In this paper, new soliton-like solutions are obtained for (2 + 1)-dimensional potential Kadomstev-Petviashvili (PKP) equation by using the symbolic computation method developed by Gao and Tian. Solitary wave solution...
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In this paper, new soliton-like solutions are obtained for (2 + 1)-dimensional potential Kadomstev-Petviashvili (PKP) equation by using the symbolic computation method developed by Gao and Tian. Solitary wave solutions obtained in [Appl. Math. Comput 123 (2001) 29] are merely a special case in this paper. The method can also be extended to other types of nolionear evolution equations in mathematical physics. (C) 2002 Elsevier Inc. All rights reserved.
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