Results 1 to 10 of about 24,526 (218)

On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions [PDF]

Heliyon, 2023
In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method.
Baoyong Guo, Yong Fang, Huanhe Dong
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Hybrid exact solutions of the (3 + 1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles

Results in Physics, 2021
In this paper, we study some exact solutions of the (3 + 1)-dimensional variable-coefficient nonlinear wave equation in liquid with gas bubbles. Based on a given transformation and the bilinear form, together with symbolic computations, we obtain the ...
Ya-Ru Guo, Ai-Hua Chen
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Exact solitary and periodic wave solutions of high-order nonlinear Schrödinger equation and their relationship with Hamilton energy

AIP Advances, 2021
In this paper, we study the exact solitary wave solutions, periodic wave solutions, and bounded rational function solution of the high-order nonlinear Schrödinger equation and the evolutional relationships between the solitary and periodic wave solutions
Weiguo Zhang, Yuli Guo, Siyu Hong, Xingqian Ling   +3 more
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Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis

Results in Physics, 2021
In this paper, we study the generalized Burgers equation with variable coefficients which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including 2-lump-type
Ziqiang Li, Jalil Manafian, Natig Ibrahimov, Afandiyeva Hajar, Kottakkaran Sooppy Nisar, Wasim Jamshed   +5 more
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Optical soliton perturbation with Kudryashov’s generalized law of refractive index and generalized nonlocal laws by improved modified extended tanh method

Alexandria Engineering Journal, 2022
In this work, the improved modified extended tanh scheme is implemented to extract exact travelling wave solutions for perturbed nonlinear Schrödinger’s equation with Kudryashov’s law of refractive index and dual form of generalized nonlocal nonlinearity.
Islam Samir, Niveen Badra, Hamdy M. Ahmed, Ahmed H. Arnous   +3 more
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New periodic exact traveling wave solutions of Camassa–Holm equation

Partial Differential Equations in Applied Mathematics, 2022
In Zhang et al. (2007) and Zhang (2021) we constructed all single-peak traveling wave solutions of the Camassa–Holm equation including some explicit solutions. In general it is a challenge to construct exact multi-peak traveling wave solutions.
Guoping Zhang
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The Jacobi elliptic function method and its application for the stochastic NNV system

Alexandria Engineering Journal, 2023
In this paper, the stochastic Nizhnik-Novikov-Veselov (NNV) system, which is a two-dimensional with a multiplicative noise in the Ito sense is studied for simple periodic wave solutions.
A. Hussain, Younes Chahlaoui, F.D. Zaman, T. Parveen, Ahmed M. Hassan   +4 more
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The nonlinear vibration and dispersive wave systems with extended homoclinic breather wave solutions

Open Physics, 2022
This article investigates the extended homoclinic (heteroclinic) breather wave solutions and interaction periodic and dark soliton solutions to the nonlinear vibration and dispersive wave systems.
Rao Xianqing, Manafian Jalil, Mahmoud K. H., Hajar Afandiyeva, Mahdi Ahmed B., Zaidi Muhaned   +5 more
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Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity

Fractal and Fractional, 2023
This paper studies the bifurcations of the exact solutions for the time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity.
Wenjing Zhu, Zijie Ling, Yonghui Xia, Min Gao   +3 more
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Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

Journal of Applied Mathematics, 2012
We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained.
Ming Song, Zhengrong Liu
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