Symmetries of solitons and general solutions of non-linear wave equations

1979 ◽  
Vol 72 (4-5) ◽  
pp. 281-283 ◽  
Author(s):  
F.J. Chinea
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
General Solutions ◽  
Non Linear ◽  
Linear Wave Equations

Uniqueness for stochastic non-linear wave equations

2007 ◽  
Vol 67 (12) ◽  
pp. 3287-3310 ◽  
Author(s):  
Martin Ondreját
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations

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

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

Some singular motions of non-Abelian Toda lattices

2000 ◽  
Vol 78 (2) ◽  
pp. 99-112
Author(s):  
W E Couch ◽  
M Surovy ◽  
R J Torrence
Keyword(s):  
Lattice Dynamics ◽  
Wave Equations ◽  
Toda Lattice ◽  
Linear Wave ◽  
General Solutions ◽  
Wave Solutions ◽  
Nonsingular Matrices ◽  
Linear Wave Equations ◽  
Singular Matrices ◽  
Toda Lattices

Motions of finite Toda lattices are known to be associated with linear wave equations whose general solutions can be expressed in terms of progressing waves, and this association is known to generalize to finite non-Abelian Toda lattices of n x n matrices and systems of n coupled linear wave equations. We present a nontrivial family of non-Abelian Toda lattice motions that can be specialized to ones that are not finite, but not infinitely extendible either, as they contain nonvanishing but singular matrices of rank (n – s). In these cases we give a natural continuation of the lattice dynamics by means of nonsingular matrices of dimension (n – s) x (n – s), and describe how to find s progressing wave solutions of the associated system of n coupled linear wave equations.PACS No.: 5.45-a

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