Results 171 to 180 of about 17,079 (203)

Multiple soliton solutions and multiple singular soliton solutions of the modified KdV equation with first-order correction

Physica Scripta, 2010
In this work, we study the modified KdV equation with first-order correction. Multiple soliton solutions and multiple singular soliton solutions are formally derived for this perturbed model. The simplified form of the bilinear method will be employed to carry out this analysis.
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The generalized KaupߝBoussinesq equation: multiple soliton solutions

Waves in Random and Complex Media, 2015
In this work, we investigate the generalized two-field Kaup–Boussinesq (KB) equation. The KB equation possesses the cubic nonlinearity that distinguishes it from the Boussinesq equation that contains quadratic nonlinearity. We use the simplified form of Hirota’s direct method to determine multiple soliton solutions and multiple singular soliton ...
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Multiple-soliton solutions and analytical solutions to a nonlinear evolution equation

Optical and Quantum Electronics, 2017
The mathematical modelling of physical systems is generally expressed by nonlinear evolution equations. Therefore, it is critical to obtain solutions to these equations. We have employed the Hirota’s method to derive multiple soliton solutions to (2+1)-dimensional nonlinear evolution equation.
Melike Kaplan, Mehmet Naci Ozer
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A coupled Ramani equation: multiple soliton solutions

Journal of Mathematical Chemistry, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multiple-soliton solutions for the Boussinesq equation

Applied Mathematics and Computation, 2007
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Resonant multiple wave solutions to some integrable soliton equations*

Chinese Physics B, 2019
To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation, the (3+1)-dimensional generalized Kadomtsev–Petviashvili (g-KP) equation, and the B-type Kadomtsev ...
Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng   +2 more
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Four (2+1)-dimensional integrable extensions of the KdV equation: Multiple-soliton and multiple singular soliton solutions

Applied Mathematics and Computation, 2009
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Higher dimensional integrable Vakhnenko–Parkes equation: multiple soliton solutions

International Journal of Numerical Methods for Heat & Fluid Flow, 2020
Purpose This study aims to develop a new (3 + 1)-dimensional Painlevé-integrable extended Vakhnenko–Parkes equation. The author formally derives multiple soliton solutions for this developed model. Design/methodology/approach The study used the simplified Hirota’s method for deriving multiple soliton solutions.
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The multiple-soliton solution of the Camassa-Holm equation

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2004
Summary: This paper refines Johnson's implementation of Constantin's method for solving the Camassa-Holm equation for a multiple-soliton solution. An analytical formula for the \(q(y)\) and an explicit relation between \(x\) and \(y\) are found. An algorithm of solving for \(u(y)\) is presented.
Li, Yishen, Zhang, Jin E.
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Multiple-soliton solutions of the perturbed KdV equation

Communications in Nonlinear Science and Numerical Simulation, 2010
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