Results 41 to 50 of about 1,094 (76)
Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions [PDF]
, 2013 In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution.
Sun, Ying-ying +2 more
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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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, 2000 We present here an overview for the Encyclopaedia of Mathematics of the various forms and properties of this system of equations together with its geometric and Lie algebraic ...
Helminck, G.F.
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The periodic b-equation and Euler equations on the circle
, 2010 In this note we show that the periodic b-equation can only be realized as an Euler equation on the Lie group Diff(S^1) of all smooth and orientiation preserving diffeomorphisms on the cirlce if b=2, i.e. for the Camassa-Holm equation.
Arnold V. I. +2 more
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Inverse Scattering Transform for the Camassa-Holm equation [PDF]
, 2006 An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data.
Adrian Constantin +21 more
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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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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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The equations of some dispersionless limit [PDF]
, 1995 This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations.
Son, Seung Hwan
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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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