Abstract
In this paper, local and nonlocal reductions of two nonisospectral Ablowitz-Kaup-Newell-Segur equations, the third order nonisospectral AKNS equation and the negative order nonisospectral AKNS equation, are studied. By imposing constraint conditions on the double Wronskian solutions of the aforesaid nonisospectral AKNS equations, various solutions for the local and nonlocal nonisospectral modified Korteweg-de Vries equation and local and nonlocal nonisospectral sine-Gordon equation are derived, including soliton solutions and Jordan block solutions. Dynamics of some obtained solutions are analyzed and illustrated by asymptotic analysis.
Highlights
Before considering the local and nonlocal reductions we reveal the bilinearization and double Wronskian solutions for the nAKNS(-1) Equation (4)
We have investigated the local and nonlocal reductions for the nAKNS(3)
By imposing constraint conditions on the two basic vectors in the double Wronskian solutions of the nAKNS(3) Equation (3) and the nAKNS(-1) Equation (4), we have presented 1-soliton solution, 2-soliton solutions and Jordan block solutions for the obtained equations
Summary
Soliton solutions for the positive order nonisospectral AKNS hierarchy were obtained through the inverse scattering transform [12]. By introducing generalization to the AKNS spectral problem (1) and considering simple symmetry reductions, several reverse space-time and reverse time nonlocal nonlinear integrable equations have been introduced [17]. These include the reverse space-time, and in some cases reverse time, nonlocal NLS, mKdV, sG, (1 + 1) and (2 + 1) dimensional three-wave interaction, derivative NLS, “loop soliton” and Davey-Stewartson equations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
