Results 1 to 10 of about 155 (137)
Periodic, n-soliton and variable separation solutions for an extended (3+1)-dimensional KP-Boussinesq equation. [PDF]
Sci Rep, 2023 An extended (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation is studied in this paper to construct periodic solution, n-soliton solution and folded localized excitation.
Shao C +5 more
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Sech 2 -type solitary waves and the stability analysis for the KdV-mKdV equation. [PDF]
Sci RepIn this article, we investigated the solitary wave solutions of the KdV–mKdV equation using Hirota’s bilinear method. Closed-form analytical single and multiple solitary wave solutions were obtained.
Liu ZG, Liu M, Zhang J.
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Partial Differential Equations in Applied Mathematics, 2022 A generalized (2+1)-dimensional BKP equation with more second order nonlinear terms is studied. The different types of lump–kink solutions and lump–soliton solutions are constructed by using a combination of Hirota’s bilinear method and Maple symbolic ...
Qiao Huang, Yehui Huang, Liqin Zhang
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Results in Physics, 2023 The purpose of this research paper is to investigate the (3+1)-dimensional Hirota bilinear equation that arises in nonlinear waves in fluid dynamics, plasma physics and shallow water waves.
Hajar F. Ismael +5 more
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Advances in Mathematical Physics, 2021 An integrable variable coefficient nonlocal nonlinear Schrödinger equation (NNLS) is studied; by employing the Hirota’s bilinear method, the bilinear form is obtained, and the N-soliton solutions are constructed.
Guiying Chen, Xiangpeng Xin, Feng Zhang
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Overview of the Kadomtsev–Petviashvili-hierarchy reduction method for solitons
Partial Differential Equations in Applied Mathematics, 2022 The Kadomtsev–Petviashvili (KP) hierarchy reduction method is a prominent direct method for deriving explicit solutions to integrable equations. This method is based on Hirota’s bilinear formulation of integrable systems, as well as the observation that ...
Bo Yang, Jianke Yang
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The Soliton Solutions and Long-Time Asymptotic Analysis for a General Coupled KdV Equation
Advances in Mathematical Physics, 2021 A general coupled KdV equation, which describes the interactions of two long waves with different dispersion relation, is considered. By employing the Hirota’s bilinear method, the bilinear form is obtained, and the one-soliton solution and two-soliton ...
Changhao Zhang, Guiying Chen
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Multiple lump solutions of the (2+1)-dimensional sawada-kotera-like equation
Frontiers in Physics, 2022 In this paper, 1-lump solution and 2-lump solution of a (2 + 1)-dimensional Sawada-Kotera-like equation are obtained by means of the Hirota’s bilinear method and long wave limit method.
Feng-Hua Qi +3 more
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Higher-Order Benjamin–Ono Model for Ocean Internal Solitary Waves and Its Related Properties
Axioms, 2023 In this study, the propagation of internal solitary waves in oceans at great depths was analyzed. Using multi-scale analysis and perturbation expansion, the basic equation is simplified to the classical Benjamin–Ono equation with variable coefficients ...
Yanwei Ren +3 more
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Lump Solutions of a Nonlinear PDE Combining with a New Fourth-Order Term Dx2Dt2∗
Advances in Mathematical Physics, 2020 A nonlinear PDE combining with a new fourth-order term Dx2Dt2 is studied. Adding three new fourth-order derivative terms and some second-order derivative terms, we formulate a combined fourth-order nonlinear partial differential equation, which possesses
Liqin Zhang, Wen-Xiu Ma, Yehui Huang
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