Results 31 to 40 of about 95 (93)
Explicit solutions of generalized nonlinear Boussinesq equations
Journal of Applied Mathematics, Volume 1, Issue 1, Page 29-37, 2001., 2001 By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components.
Doğan Kaya
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, 2014 . Higher KdV flows on spaces of closed equicentroaffine plane curves are studied and it is shown that the flows are described as certain multi-Hamiltonian systems on the spaces.
Kurose, T. +3 more
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Chains of KP, semi‐infinite 1‐Toda lattice hierarchy and Kontsevich integral
Journal of Applied Mathematics, Volume 1, Issue 4, Page 175-193, 2001., 2001 There are well‐known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1‐Toda lattice hierarchy.
L. A. Dickey
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Results in Physics, 2016 The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation.
Chen Yue, Aly Seadawy, Dianchen Lu
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A Study of Third-order KdV and mKdV Equations by Laplace Decomposition Method
, 2022 In this article, the Laplace decomposition method is implementedto solve nonlinear partial differential equations. Third-order KdVand mKdV equations with initial conditions have been considered to checkthe validity of the proposed method.
S. S. Handibag +1 more
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Three‐dimensional Korteweg‐de Vries equation and traveling wave solutions
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 6, Page 379-384, 2000., 2000 The three‐dimensional power Korteweg‐de Vries equation [ut+unux+uxxx] x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n = 1 and n = 2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson′s summation ...
Kenneth L. Jones
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Explicit Formulas to the Solutions of Several Equations of Mathematical Physics [PDF]
, 2014 [Popivanov Petar; Попиванов Петър]Explicit formulas to the solutions of several equations of mathematical physics including semilinear multidimensional Klein-Gordon equation, the wave equation, Kadomtsev-Petviashvili equation and cubic first order ...
Popivanov, Petar
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New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation
International Journal of Differential Equations, Volume 2025, Issue 1, 2025.In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=00,β≠ is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σ(t) ~ |t|−1/2 for the uniform radius of spatial analyticity of solutions to the ...
Tegegne Getachew, Jaume Giné
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 643-648, 1999., 1999 The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions.
Kenneth L. Jones, Yunkai Chen
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.In this work, consideration is given to the initial value problem associated with the periodic fifth‐order KdV–BBM equation. It is shown that the uniform radius of spatial analyticity σ(t) of solution at time t is bounded from below by ct−2/3 (for some c > 0), given initial data η0 that is analytic on the circle and has a uniform radius of spatial ...
Tegegne Getachew, Giovanni P. Galdi
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