Results 41 to 50 of about 95 (93)
Addendum to a paper of Craig and Goodman
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 825-827, 1994., 1994 In [1], Craig and Goodman develop the geometrical optics solution of the linearized Korteweg‐deVries equation away from caustic, or turning, points. Here we develop an analogous solution valid at caustic points.
Arthur D. Gorman
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Bäcklund–Darboux Transformations and Discretizations of Super KdV Equation
, 2014 . For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.
Xue, L.L. +3 more
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems. Although the origin of nonlinear evolution equations dates back to ancient times, significant developments have been made in ...
Murat Koparan, Salim A. Messaoudi
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International Journal of Stochastic Analysis, Volume 7, Issue 1, Page 1-12, 1994., 1993 We discuss the existence, uniqueness, and continuous dependence on data, of anti‐periodic traveling wave solutions to higher order two‐dimensional equations of Korteweg‐deVries type.
Sergiu Aizicovici +2 more
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Forum of Mathematics, Sigma, 2015 We introduce a novel solution concept, denoted ${\it\alpha}$-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system on the line with ...
KATRIN GRUNERT +2 more
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On radial sine-Gordon breathers
, 2000 The problem of the existence of radial sine-Gordon breathers (i.e. radial solutions which are periodic in time and decay at infinity with respect to the spatial variable) in the (d + 1)-dimensional case (where d > 1) is considered.
Alfimov, G.L., Vazquez, L., Evans, Andy
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Decay Rate on the Radius of Spatial Analyticity to Solutions for the Modified Camassa–Holm Equation
Journal of Mathematics, Volume 2025, Issue 1, 2025.The initial value problem associated with the modified Camassa–Holm equation for initial data u0(x) that is analytic on the line and having uniform radius of spatial analyticity σ0 is considered. We have shown the persistence of the radius of spatial analyticity till some time δ.
Tegegne Getachew, Yongqiang Fu
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The initial-value problem for a Gardner-type equation
Advanced Nonlinear StudiesDiscussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry +4 more
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Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves
Results in Physics, 2019 In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived ...
Essam. R. El-Zahar, Hilmi Demiray
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Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation
Advances in Nonlinear AnalysisIn this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect.
Moon Byungsoo, Yang Chao
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