Nonlinear multi-wave coupling and resonance in elastic structures

The occurrence of resonance at the expense of nonlinear multi-wave coupling is discussed.Kaup P. J., Reiman A. and Bers A. Space-time evolution of nonlinear three-wave interactions.Resonance in multi-frequency systems.In the case of resonance the solution to eqs.(12) cannot be simply reduced to eqs. (13) , since the system (12) experiences a resonance.The resonance plays a principal role in the dynamical behavior of most physical systems.Nonlinear Dynamics, 4 (2) , 72-102 (in Russian) .When the combinations ; otherwise, the problem of small divisors (resonances) appears.Self-action of a single wave as and .Where the nonlinear terms . Here are the uniform -th order polynomials.