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Deriving N-soliton solutions via constrained flows [PDF]
Journal of Physics A: Mathematical and General, 2000 The soliton equations can be factorized by two commuting x- and t-constrained flows. We propose a method to derive N-soliton solutions of soliton equations directly from the x- and t-constrained flows.Comment: 8 pages, AmsTex, no figures, to be published
Ablowitz M +13 more
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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
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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
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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
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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 +5 more
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Soliton solutions by means of Hirota bilinear forms
Partial Differential Equations in Applied Mathematics, 2022 The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various ...
Wen-Xiu Ma
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The N-soliton solution of a generalised Vakhnenko equation [PDF]
Glasgow Mathematical Journal, 2001 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.
Morrison, A.J., Parkes, E.J.
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Results in Physics, 2021 Based on the N-soliton solutions, the resonant line wave soliton and interaction solutions are derived through some constraints in the (2+1)-dimensional nonlinear wave equation. General resonant line wave soliton solutions are firstly presented and their
Qingqing Chen +3 more
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Complexity, 2020 In this paper, a new generalized semidiscrete integrable system with time-varying coefficients is analytically studied. Firstly, the generalized semidiscrete system is derived from a semidiscrete matrix spectral problem by embedding finite time-varying ...
Sheng Zhang, Sen Zhao, Bo Xu
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M-Breather, Lumps, and Soliton Molecules for the 2+1-Dimensional Elliptic Toda Equation
Advances in Mathematical Physics, 2021 The 2+1-dimensional elliptic Toda equation is a higher dimensional generalization of the Toda lattice and also a discrete version of the Kadomtsev-Petviashvili-1 (KP1) equation. In this paper, we derive the M-breather solution in the determinant form for
Yuechen Jia, Yu Lu, Miao Yu, Hasi Gegen
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