Results 11 to 20 of about 3,171,507 (251)
The “good” Boussinesq equation : long-time asymptotics [PDF]
Analysis & PDE, 2023 We consider the initial-value problem for the ``good'' Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a $3 \times 3$-matrix Riemann-Hilbert problem. We establish formulas for the long-time asymptotics of the solution by performing a Deift-Zhou steepest descent analysis of ...
Charlier, Christophe +2 more
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Traveling wave solutions to the Boussinesq equation via Sardar sub-equation technique
AIMS Mathematics, 2022 In present study, the Boussinesq equation is obtained by means of the Sardar Sub-Equation Technique (SSET) to create unique soliton solutions containing parameters. Using this technique, different solutions are obtained, such as the singular soliton, the
Hamood-Ur-Rahman +9 more
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Fractional Analysis of Nonlinear Boussinesq Equation under Atangana-Baleanu-Caputo Operator
Symmetry, 2022 This article proposed two novel techniques for solving the fractional-order Boussinesq equation. Several new approximate analytical solutions of the second- and fourth-order time-fractional Boussinesq equation are derived using the Laplace transform and ...
Sultan Alyobi +4 more
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Long-time asymptotics of the good Boussinesq equation with qxx-term and its modified version
Journal of Mathematics and Physics, 2022 Two modified Boussinesq equations along with their Lax pairs are proposed by introducing the Miura transformations. The modified good Boussinesq equation with initial condition is investigated by the Riemann–Hilbert method.
Deng Wang, Xiaodong Zhu
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The "good" Boussinesq equation: a Riemann-Hilbert approach [PDF]
Indiana University Mathematics Journal, 2020 We develop an inverse scattering transform formalism for the "good" Boussinesq equation on the line. Assuming that the solution exists, we show that it can be expressed in terms of the solution of a $3 \times 3$ matrix Riemann-Hilbert problem.
C. Charlier, J. Lenells
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Advances in Mathematical Physics, 2021 The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2+1-dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2+1-
Bo Ren
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On the periodic “good” Boussinesq equation [PDF]
Proceedings of the American Mathematical Society, 2009 We study the well-posedness of the initial-value problem for the periodic nonlinear “good” Boussinesq equation. We prove that this equation is locally well posed for initial data in Sobolev spaces H s ( T ) H^s(\mathbb {T}) for s > −
Farah, Luiz Gustavo, Scialom, Márcia
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The coupled Boussinesq equation and its Darboux transformation on the time–space scale
Frontiers in Physics, 2022 Gel’fand-Dikii (GD) formalism is an approach for generating integrable systems in terms of fractional powers of the δ differential operator. In this paper, it extends the GD formalism associated with the third-order δ differential operator L to the time ...
Xiaoqian Huang, Yong Zhang, Huanhe Dong
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Mathematics, 2023 Herein, we mainly employ the fixed point theorem and Lax-Milgram theorem in functional analysis to prove the existence and uniqueness of generalized and mixed finite element (MFE) solutions for two-dimensional steady Boussinesq equation.
Zhendong Luo +3 more
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Mathematics, 2020 This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived.
Juan Luis García Guirao +2 more
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