Results 11 to 20 of about 292 (66)
Alexandria Engineering Journal, 2023 The generalized Hirota-Satsuma coupled KdV system with fractional-order derivative plays a significant role to simulate the interaction of nearby identical-weight particles in a crystal lattice structure, two long waves interaction with different ...
H.M. Shahadat Ali +4 more
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On Transformations of the Rabelo Equations [PDF]
, 2007 We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations.
Sakovich, Anton, Sakovich, Sergei
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Journal of Ocean Engineering and Science, 2019 In this article, two different methods, namely sub-equation method and residual power series method, have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations, which is a coupled KdV model.
Ali Kurt +6 more
doaj +1 more source
Multi-integral representations for associated Legendre and Ferrers functions
, 2020 For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas.
Cohl, Howard S. +1 more
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On a Whitham-Type Equation [PDF]
, 2009 The Hunter-Saxton equation and the Gurevich-Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions are obtained ...
Sakovich, Sergei
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Eigenstructure of the equilateral triangle. Part III. The Robin problem
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 16, Page 807-825, 2004., 2004 Lamé′s formulas for the eigenvalues and eigenfunctions of the Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the Robin boundary condition. They are shown to form a complete orthonormal system. Various properties of the spectrum and modal functions are explored.
Brian J. McCartin
wiley +1 more source
Bäcklund transformations for several cases of a type of generalized KdV equation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 63, Page 3369-3377, 2004., 2004 An alternate generalized Korteweg‐de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting,
Paul Bracken
wiley +1 more source
An approximate analytic solution of a particular boundary value problem
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 8, Page 513-520, 2001., 2001 This note is concerned with the three‐dimensional quasi‐steady‐state heat conduction equation subject to certain boundary conditions in the whole x′y′‐plane and finite in z′‐direction. This type of boundary value problem arises in laser welding process. The solution to this problem can be represented by an integral using Fourier analysis. This integral
Ugur Tanriver, Aravinda Kar
wiley +1 more source
Some properties of the Feynman‐Kac functional
International Journal of Stochastic Analysis, Volume 8, Issue 1, Page 1-10, 1995., 1994 The Feynman‐Kac formula and its connections with classical analysis were initiated in the now celebrated paper [6] of M. Kac. It soon became obvious that the formula provides a powerful tool for solving partial differential equations by running the Brownian motion process. K.L. Chung and K.M.
S. Graversen +2 more
wiley +1 more source
On the central quadric ansatz: integrable models and Painleve reductions [PDF]
, 2012 It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called
A Zhang +11 more
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