A CLASS OF SPECIAL EXACT SOLUTIONS OF SOME HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS

In this paper, the separation transformation approach is extended to some high dimensional non-linear wave equations, such as the (N+1)-dimensional Zhiber–Shabat equation, the generalized (N+1)-dimensional complex non-linear Klein–Gordon equation and the generalized (N+1)-dimensional Toda lattice equation. As a result, a class of special exact solutions of these equations are obtained. The solutions obtained contain one or two arbitrary functions which may lead to abundant structures of the high dimensional non-linear wave equations.

Download Full-text

Exact solutions of the non-linear wave equations arising in mechanics

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(90)90140-6 ◽

1990 ◽

Vol 54 (3) ◽

pp. 372-375 ◽

Cited By ~ 21

Author(s):

N.A. Kudryashov

Keyword(s):

Exact Solutions ◽

Wave Equations ◽

Linear Wave ◽

Non Linear ◽

Linear Wave Equations

Download Full-text

Exact solutions of non-linear Klein–Gordon equation with non-constant coefficients through the trial equation method

Journal of Mathematical Chemistry ◽

10.1007/s10910-021-01220-y ◽

2021 ◽

Author(s):

Jorge E. Macías-Díaz ◽

María G. Medina-Guevara ◽

Héctor Vargas-Rodríguez

Keyword(s):

Exact Solutions ◽

Gordon Equation ◽

Equation Method ◽

Trial Equation Method ◽

Non Linear ◽

Klein Gordon ◽

Constant Coefficients ◽

Klein Gordon Equation

Download Full-text

Unsolved Problems in the Theory of Non-Linear Wave Equations

Many Degrees of Freedom in Field Theory ◽

10.1007/978-1-4615-8924-2_5 ◽

1978 ◽

pp. 147-162 ◽

Cited By ~ 1

Author(s):

Michael Reed

Keyword(s):

Wave Equations ◽

Linear Wave ◽

Non Linear ◽

Linear Wave Equations

Download Full-text

Uniqueness for stochastic non-linear wave equations

Nonlinear Analysis ◽

10.1016/j.na.2006.10.012 ◽

2007 ◽

Vol 67 (12) ◽

pp. 3287-3310 ◽

Cited By ~ 1

Author(s):

Martin Ondreját

Keyword(s):

Wave Equations ◽

Linear Wave ◽

Non Linear ◽

Linear Wave Equations

Download Full-text

Global estimates for non-linear wave equations and linear wave equations with non-linear boundary constraints

Ordinary and Partial Differential Equations - Lecture Notes in Mathematics ◽

10.1007/bfb0087362 ◽

1976 ◽

pp. 438-451 ◽

Cited By ~ 1

Author(s):

B. D. Sleeman

Keyword(s):

Wave Equations ◽

Linear Wave ◽

Linear Boundary ◽

Boundary Constraints ◽

Non Linear ◽

Global Estimates ◽

Linear Wave Equations

Download Full-text

Non-linear wave equations for free surface flow over a bump

Coastal Engineering Journal ◽

10.1080/21664250.2020.1712837 ◽

2020 ◽

Vol 62 (2) ◽

pp. 159-169

Author(s):

Shino Sakaguchi ◽

Keisuke Nakayama ◽

Thuy Thi Thu Vu ◽

Katsuaki Komai ◽

Peter Nielsen

Keyword(s):

Free Surface ◽

Wave Equations ◽

Free Surface Flow ◽

Surface Flow ◽

Linear Wave ◽

Non Linear ◽

Linear Wave Equations

Download Full-text

Global existence of low regularity solutions of non-linear wave equations

Mathematische Zeitschrift ◽

10.1007/bf02572346 ◽

1995 ◽

Vol 219 (1) ◽

pp. 1-19 ◽

Cited By ~ 3

Author(s):

Vladimir Georgiev ◽

Pedro Paulo Schirmer

Keyword(s):

Global Existence ◽

Wave Equations ◽

Linear Wave ◽

Low Regularity ◽

Non Linear ◽

Low Regularity Solutions ◽

Linear Wave Equations

Download Full-text

Global Spherically Symmetric Solutions of Non-linear Wave Equations with Null Condition on Extremal Reissner–Nordström Spacetimes

International Mathematics Research Notices ◽

10.1093/imrn/rnv240 ◽

2015 ◽

Vol 2016 (11) ◽

pp. 3279-3355 ◽

Cited By ~ 4

Author(s):

Yannis Angelopoulos

Keyword(s):

Wave Equations ◽

Linear Wave ◽

Spherically Symmetric ◽

Null Condition ◽

Spherically Symmetric Solutions ◽

Non Linear ◽

Linear Wave Equations

Download Full-text

Analyticity of global attractors and determining nodes for a class of damped non-linear wave equations

Sbornik Mathematics ◽

10.1070/sm2000v191n10abeh000519 ◽

2000 ◽

Vol 191 (10) ◽

pp. 1541-1559 ◽

Cited By ~ 2

Author(s):

I D Chueshov

Keyword(s):

Wave Equations ◽

Global Attractors ◽

Linear Wave ◽

Non Linear ◽

Linear Wave Equations ◽

Determining Nodes

Download Full-text

Weakly non-linear, slowly varying waves and their instabilities

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100050982 ◽

1972 ◽

Vol 72 (1) ◽

pp. 95-104 ◽

Cited By ~ 1

Author(s):

R. Grimshaw

Keyword(s):

Variational Principle ◽

Gordon Equation ◽

Transport Equations ◽

Linear Wave ◽

Leading Order ◽

Non Linear ◽

Klein Gordon ◽

Wave Trains ◽

Klein Gordon Equation

AbstractA non-linear Klein–Gordon equation is used to discuss the theory of slowly varying, weakly non-linear wave trains. An averaged variational principle is used to obtain transport equations for the slow variations which incorporate the leading order modulation and non-linear terms. Linearized transport equations are used to discuss instabilities.

Download Full-text