The generalized nonlinear SchrÃ¶dinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classicalâ€¦ (More)

Two numerical methods are presented for the periodic initial-value problem of the long waveâ€“short wave interaction equations describing the interaction between one long longitudinal wave and twoâ€¦ (More)

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness andâ€¦ (More)

where u and Ï†1, Ï†2 are, respectively, the complexand the real-valued functions of spatial coordinates x, y and the time t. The parameters Ïƒ, Îº, Î³,m1,m2, Î», n are real constants and Ïƒ is normalized asâ€¦ (More)

Blow-up solutions for the purely elliptic generalized Davey-Stewartson system are studied by using a relaxation numerical method. The numerical method is based on an implicit finite-difference schemeâ€¦ (More)

Many equations can be expressed as a cubic nonlinear SchrÃ¶dinger (NLS) equation with additional terms, such as the Davey-Stewartson (DS) system [1]. As it is the case for the NLS equation, theâ€¦ (More)