Behaviour of the extended modified Volterra lattice-Reductions to generalised mKdV and NLS equations

Abstract We consider the first member of an extended modified Volterra lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptotic analysis to consider the long wavelength limits of the system. By considering various magnitudes for the parameters involved, we derive reduced equations related to the modified Korteweg-de Vries and nonlinear Schrodinger equations.

[1]  A. Degasperis,et al.  Extension of the spectral transform method for solving nonlinear evolution equations , 1978 .

[2]  P. R. Gordoa,et al.  A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions , 2005 .

[3]  Allan P. Fordy,et al.  Soliton Theory: A Survey of Results , 1990 .

[4]  Lena Vogler,et al.  The Direct Method In Soliton Theory , 2016 .

[5]  Combined breathing–kink modes in the FPU lattice , 2011 .

[6]  P. R. Gordoa,et al.  Non-isospectral lattice hierarchies in 2+1 dimensions and generalized discrete Painlevé hierarchies , 2005 .

[7]  A. Hasegawa,et al.  Nonlinear pulse propagation in a monomode dielectric guide , 1987 .

[8]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[9]  P. R. Gordoa,et al.  Behaviour of the extended Volterra lattice , 2014, Commun. Nonlinear Sci. Numer. Simul..

[10]  P. R. Gordoa,et al.  New 2+1 dimensional nonisospectral Toda lattice hierarchy , 2007 .

[11]  Michel Remoissenet,et al.  Waves called solitons , 1994 .

[12]  A. Degasperis,et al.  Exact solution via the spectral transform of a generalization with linearlyx-dependent coefficients of the nonlinear Schrödinger equation , 1978 .

[13]  Antonio Degasperis,et al.  Conservation laws for classes of nonlinear evolution equations solvable by the spectral transform , 1978 .

[14]  A. Degasperis,et al.  Exact solution via the spectral transform of a generalization with linearlyx-dependent coefficients of the modified Korteweg-de-Vires equation , 1978 .

[15]  P. Drazin,et al.  Solitons: An Introduction , 1989 .

[16]  P. R. Gordoa,et al.  Behaviour of the extended Toda lattice , 2015, Commun. Nonlinear Sci. Numer. Simul..

[17]  G. Lamb.  Elements of soliton theory , 1980 .

[18]  L. Debnath.  Solitons and the Inverse Scattering Transform , 2012 .