Results 31 to 40 of about 3,171,507 (251)
The (3+1)-dimensional Boussinesq equation: Novel multi-wave solutions
Results in Physics, 2023 The Boussinesq equation is a partial differential equation that describes the behavior of waves in shallow water. In this paper, we address some new dynamical behaviors to the (3+1)-dimensional Boussinesq equation, which are not constructed beforehand ...
Hajar Farhan Ismael
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Generalized exponential rational function method to the fractional shallow water wave phenomena
Partial Differential Equations in Applied Mathematics, 2023 In this study we introduce the fractional shallow water wave phenomena, namely, the new extended (2 + 1)-dimensional fractional Boussinesq equation and in the following we apply the generalized exponential rational function for extracting the soliton ...
Ahmad Sharif, Mostafa Eslami
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, 2015 Boussinesq equation belongs to Korteweg-de Vries kind of equations (Han & Yarkony, 2011). Equation describes the motion of long waves in two dimensions under the gravitation (Han & Yarkony, 2011). Here, we differentiate u = u(x, t) to the needed order.
Seilova, Dana +3 more
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Two exponential-type integrators for the “good” Boussinesq equation [PDF]
Numerische Mathematik, 2019 We introduce two exponential-type integrators for the “good” Boussinesq equation. They are of orders one and two, respectively, and they require lower spatial regularity of the solution compared to classical exponential integrators.
A. Ostermann, Chunmei Su
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Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition [PDF]
, 2002 We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation, the $\lambda \
Ablowitz M +15 more
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Conservation laws of some lattice equations
, 2012 We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schr\"{o}dinger ...
Cheng, Jun-wei, Zhang, Da-jun
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Miura transformation for the “good” Boussinesq equation
Studies in Applied Mathematics, 2023 AbstractIt is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura‐type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second‐order
Charlier, Christophe, Lenells, J.
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Journal of Applied Mathematics, 2014 We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bidirectional propagation of small amplitude and long capillary-gravity waves on the surface ...
Changming Song, Jina Li, Ran Gao
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The discrete potential Boussinesq equation and its multisoliton solutions
, 2009 An alternate form of discrete potential Boussinesq equation is proposed and its multisoliton solutions are constructed. An ultradiscrete potential Boussinesq equation is also obtained from the discrete potential Boussinesq equation using the ...
Ablowitz MJ +7 more
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On Schrödinger-Boussinesq equations
Advances in Differential Equations, 2004 We study local and global well-posedness for the initial-value problem associated to the one-dimensional Schrödinger-Boussinesq equations in low regularity spaces. To establish these results we make use of sharp $L^p$-$L^q$ estimates.
Linares, F., Navas, A.
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