Integrability of nonlinear wave equations and solvability of their initial value problem

J.P. BORGNA; A. DEGASPERIS; M. DE LEO; D. RIAL

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2012

0022-2488

We investigate one particular prototypical system of evolution equations in 1+1dimensions, which models the (nonlocal) interaction of two waves in quadratic non-linear media. These equations are integrable as they possess a Lax pair. We consider the spectral method of solving the associated initial value problem and, as recently pointed out, we show that generically the associated initial value problem cannot be linearized. We further elaborate on the integrability issue for this model by displaying the corresponding conservation laws and the motion of a particular soliton.