Averaging of weakly nonlinear hyperbolic systems with nonuniform integral means

1991 ◽  
Vol 43 (5) ◽  
pp. 566-573
Author(s):  
A. V. Krylov
Keyword(s):  
Hyperbolic Systems ◽  
Integral Means ◽  
Weakly Nonlinear ◽  
Nonlinear Hyperbolic Systems

ASYMPTOTIC METHOD FOR APPROXIMATION OF RESONANT INTERACTION OF NONLINEAR MULTIDIMENSIONAL HYPERBOLIC WAVES

2008 ◽  
Vol 13 (1) ◽  
pp. 47-54 ◽  
Author(s):  
A. Krylovas
Keyword(s):  
Asymptotic Method ◽  
Hyperbolic Systems ◽  
Resonant Interaction ◽  
Method Of Averaging ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Hyperbolic Waves ◽  
Wave Problems ◽  
Nonlinear Hyperbolic Systems

A method of averaging along characteristics of weakly nonlinear hyperbolic systems, which was presented in earlier works of the author for one dimensional waves, is generalized for some cases of multidimensional wave problems. In this work we consider such systems and discuss a way to use the internal averaging along characteristics for new problems of asymptotical integration.

scholarly journals Asymptotical analysis of generalized Hirota–Satsuma type system

2010 ◽  
Vol 51 ◽  
Author(s):  
Rima Kriauzienė ◽  
Aleksandras Krylovas
Keyword(s):  
Asymptotic Analysis ◽  
Nonlinear Waves ◽  
Hyperbolic Systems ◽  
Type System ◽  
Resonance Case ◽  
Weakly Nonlinear ◽  
Coupled Equations ◽  
De Vries ◽  
Asymptotical Analysis ◽  
Nonlinear Hyperbolic Systems

Paper deals with the nonlinear coupled equations of the well known in the literature Hirota–Satsuma type system. The asymptotic analysis of this system, which is based on the principle of two scales and on averaging of weakly nonlinear hyperbolic systems along characteristics is presented in the paper. The asymptotic analysis shown that the system disintegrates on three independent Korteweg–de Vries equations in the non-resonance case, and the system describes an interaction of periodical nonlinear waves in the resonance case.

scholarly journals Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems

2010 ◽  
Vol 229 (18) ◽  
pp. 6485-6511 ◽  
Author(s):  
J. Tryoen ◽  
O. Le Maître ◽  
M. Ndjinga ◽  
A. Ern
Keyword(s):  
Hyperbolic Systems ◽  
Galerkin Methods ◽  
Nonlinear Hyperbolic Systems
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