Results 1 to 10 of about 902,254 (275)

The N-loop soliton solutions for (2+1)-dimensional Vakhnenko equation [PDF]

Glasgow Mathematical Journal, 2017
The N-soliton solution of a generalised Vakhnenko equation is found, where N is an arbitrary positive integer. The solution, which is obtained by using a blend of transformations of the independent variables and Hirota's method, is expressed in terms of a Moloney & Hodnett (1989) type decomposition.
Bangqing Li, Yu‐Lan Ma, Lipo Mo, Ying-Ying Fu   +3 more
semanticscholar   +4 more sources

Novel complex N-soliton and lump solutions for nonlocal breaking equation

Results in Physics, 2022
The Hirota bilinear method is applied to construct the new dynamics of complex N-soliton solutions for a nonlocal breaking equation. By using the auxiliary traveling wave function, the different-order soliton solutions, bifurcation solutions and lump ...
Shaofu Wang
doaj   +2 more sources

Soliton, breather, lump and their interaction solutions of the ( 2+1 $2+1$)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

Advances in Difference Equations, 2019
In this work, the ( 2+1 $2+1$)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation is investigated. Hirota’s bilinear method is used to determine the N-soliton solutions for this equation, from which the M-lump solutions are obtained by using long ...
Yaqing Liu, Xiao-Yong Wen
doaj   +2 more sources

The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions

Abstract and Applied Analysis, 2019
The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of (N+1)×(N+1) determinant and N×N determinant, and the ...
Siqi Xu
doaj   +4 more sources

High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation [PDF]

Communications in nonlinear science & numerical simulation, 2022
A series of new soliton solutions are presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann Hilbert method and transformation relationship.
Huijuan Zhou, Yong Chen
semanticscholar   +1 more source

Exact analytical soliton solutions of N-component coupled nonlinear Schrödinger equations with arbitrary nonlinear parameters. [PDF]

Physical Review E, 2022
Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not hold in real physical systems. We
Ning Mao, Li-Chen Zhao
semanticscholar   +1 more source

N-soliton, breather, M-lump and interaction dynamics for a (2 + 1)-dimensional KdV equation with variable coefficients

Results in Physics, 2023
The main purpose of this paper is to learn N-soliton, M-lump, breather solutions and interaction solutions for a KdV equation with variable coeffificients.
Deniu Yang
doaj   +1 more source

Soliton solutions and their degenerations in the (2+1)-dimensional Hirota–Satsuma–Ito equations with time-dependent linear phase speed

Nonlinear dynamics, 2023
This paper focuses on the exact soliton solutions of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equations with time-dependent linear phase speed.
Xin Chen, Yaqing Liu, Jianhong Zhuang
semanticscholar   +1 more source

Abundant soliton wave solutions and the linear superposition principle for generalized (3+1)-D nonlinear wave equation in liquid with gas bubbles by bilinear analysis

Results in Physics, 2022
In this article, we study the generalized (3+1)-dimensional nonlinear wave equation where is investigated in soliton theory and by employing the Hirota’s bilinear method the bilinear form is obtained, and the N-soliton solutions are constructed.
Guiping Shen, Jalil Manafian, Dinh Tran Ngoc Huy, Kottakkaran Sooppy Nisar, Mostafa Abotaleb, Nguyen Dinh Trung   +5 more
doaj   +1 more source

Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies

Symmetry, 2021
This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms.
Liming Ling, W. Ma
semanticscholar   +1 more source