Results 21 to 30 of about 1,175 (77)
An accurate and efficient local one-dimensional method for the 3D acoustic wave equation
Demonstratio Mathematica, 2022 We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations ...
Wu Mengling, Jiang Yunzhi, Ge Yongbin
doaj +1 more source
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
doaj +1 more source
Multiplicity and structures for traveling wave solutions of the Kuramoto‐Sivashinsky equation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 70, Page 3839-3848, 2004., 2004 The Kuramoto‐Sivashinsky (KS) equation is known as a popular prototype to represent a system in which the transport of energy through nonlinear mode coupling produces a balance between long wavelength instability and short wavelength dissipation. Existing numerical results indicate that the KS equation admits three classes (namely, regular shock ...
Bao-Feng Feng
wiley +1 more source
Results in Physics, 2021 In the current article, we will apply the scaling invariance technique to find conservation laws (CLs) for the nonlinear Chiral Schrödinger equation (NLCSE) with variable coefficients and the (2+1)-dimensional Maccari system.
Azhar Bashir +5 more
doaj +1 more source
The second‐order Klein‐Gordon field equation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 69, Page 3775-3781, 2004., 2004 We introduce and discuss the generalized Klein‐Gordon second‐order partial differential equation in the Robertson‐Walker space‐time, using the Casimir second‐order invariant operator written in hyperspherical coordinates. The de Sitter and anti‐de Sitter space‐times are recovered by means of a convenient choice of the parameter associated to the space ...
D. Gomes, E. Capelas De Oliveira
wiley +1 more source
Mathematical Problems in Engineering, Volume 2004, Issue 3, Page 185-195, 2004., 2004 This paper presents an integral solution of the generalized one‐dimensional equation of energy transport with the convective term.The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders).
Vladimir V. Kulish
wiley +1 more source
New singular solutions of Protter′s problem for the 3D wave equation
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 315-335, 2004., 2004 In 1952, for the wave equation,Protter formulated some boundary value problems (BVPs), which are multidimensional analogues of Darboux problems on the plane. He studied these problems in a 3D domain Ω0, bounded by two characteristic cones Σ1 and Σ2,0 and a plane region Σ0. What is the situation around these BVPs now after 50 years?
M. K. Grammatikopoulos +2 more
wiley +1 more source
On the existence of maximizers for a family of Restriction Theorems
, 2010 We prove the existence of maximizers for a general family of restrictions operators, up to the end-point.
Fanelli, Luca +2 more
core +1 more source
Mathematical Problems in Engineering, Volume 2003, Issue 4, Page 173-179, 2003., 2003 The relationship between the local temperature and the local heat flux has been established for the homogeneous hyperbolic heat equation. This relationship has been written in the form of a convolution integral involving the modified Bessel functions.
Vladimir V. Kulish, Vasily B. Novozhilov
wiley +1 more source
Method of replacing the variables for generalized symmetry of the D′Alembert equation
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 149-155, 2002., 2002 We show that by the generalized understanding of symmetry, the D′Alembert equation for one component field is invariant with respect to arbitrary reversible coordinate transformations.
Gennadii A. Kotel′nikov
wiley +1 more source