Nonresonant Mode Coupling for Classes of Kortewegde Vries Equations
Abstract
The method of mode coupling in third order is applied to generalized Kortewegde Vries equations. These equations contain terms which are each a product of a function of the dependent variable u times one space derivative of u, up to a derivative of the fifth order. The resulting amplitude and phase equations are then specialized to three different classes of equations. For equations of the first class the amplitudes do not change, although all modes are coupled for the determination of the phases. For equations of the second class, all amplitude equations are truly coupled and the phases are constant. Finally, for equations of the third class, which includes the KdV equation, each mode behaves as if it were the only one present, so that only selfmodulation is possible.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 December 1979
 DOI:
 10.1143/JPSJ.47.2007
 Bibcode:
 1979JPSJ...47.2007V
 Keywords:

 Coupled Modes;
 KortewegDevries Equation;
 Nonresonance;
 Wave Interaction;
 Amplitudes;
 Nonlinear Equations;
 Partial Differential Equations;
 Phase Deviation;
 Plane Waves;
 Wave Equations;
 Thermodynamics and Statistical Physics