Results 21 to 30 of about 264 (44)
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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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
core +5 more sources
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
Exact Wave Functions for Generalized Harmonic Oscillators [PDF]
, 2011 We transform the time-dependent Schroedinger equation for the most general variable quadratic Hamiltonians into a standard autonomous form. As a result, the time-evolution of exact wave functions of generalized harmonic oscillators is determined in terms
Lanfear, Nathan +2 more
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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 a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability [PDF]
, 2010 Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm.
Golenia, Jolanta +3 more
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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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