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Fractional Integrable and Related Discrete Nonlinear Schrödinger Equations
Mark J. Ablowitz, Joel B. Been, Lincoln D. Carr
Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schrödinger equations are key to the intersection of nonlinear dynamics and fractional calculu…
Fractional Integrable Nonlinear Soliton Equations
Mark J. Ablowitz, Joel B. Been, Lincoln D. Carr
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenti…
Integrable Fractional Modified Korteweg-de Vries, Sine-Gordon, and Sinh-Gordon Equations
Mark J. Ablowitz, Joel B. Been, Lincoln D. Carr
The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended to fraction…