ترغب بنشر مسار تعليمي؟ اضغط هنا

Solutions to integrable space-time shifted nonlocal equations

112   0   0.0 ( 0 )
 نشر من قبل Da-jun Zhang
 تاريخ النشر 2021
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper we present a reduction technique based on bilinearization and double Wronskians (or double Casoratians) to obtain explicit multi-soliton solutions for the integrable space-time shifted nonlocal equations introduced very recently by Ablowitz and Musslimani in [Phys. Lett. A, 2021]. Examples include the space-time shifted nonlocal nonlinear Schrodinger and modified Korteweg-de Vries hierarchies and the semi-discrete nonlinear Schrodinger equation. It is shown that these nonlocal integrable equations with or without space-time shift(s) reduction share same distributions of eigenvalues but the space-time shift(s) brings new constraints to phase terms in solutions.



قيم البحث

اقرأ أيضاً

167 - Andrei K. Svinin 2021
In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for infinite class of difference equations. We also provide an example of such a solution that is related to sequence generated by second-order linear recurrent relations.
In this paper, the partially party-time ($PT$) symmetric nonlocal Davey-Stewartson (DS) equations with respect to $x$ is called $x$-nonlocal DS equations, while a fully $PT$ symmetric nonlocal DSII equation is called nonlocal DSII equation. Three kin ds of solutions, namely breather, rational and semi-rational solutions for these nonlocal DS equations are derived by employing the bilinear method. For the $x$-nonlocal DS equations, the usual ($2+1$)-dimensional breathers are periodic in $x$ direction and localized in $y$ direction. Nonsingular rational solutions are lumps, and semi-rational solutions are composed of lumps, breathers and periodic line waves. For the nonlocal DSII equation, line breathers are periodic in both $x$ and $y$ directions with parallels in profile, but localized in time. Nonsingular rational solutions are ($2+1$)-dimensional line rogue waves, which arise from a constant background and disappear into the same constant background, and this process only lasts for a short period of time. Semi-rational solutions describe interactions of line rogue waves and periodic line waves.
322 - A. S. Fokas , J. Lenells 2021
We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schrodinger equation as a model example, we show that the solution of the initial value problem on the circle can be expressed in terms of the solution of a Riemann-Hilbert problem whose formulation involves quantities which are defined in terms of the initial data alone. Our approach provides an effective solution of the problem on the circle which is conceptually analogous to the solution of the problem on the line via the inverse scattering transform.
155 - Alexei Rybkin 2011
We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles qs which are, in a certain sense, essentially bounded from below and q(x)=O(e^{-cx^{{epsilon}}}),xrightarrow+infty, with some positive c a nd {epsilon}. Using the inverse scattering transform, we show that the KdV flow turns such initial data into a function which is (1) meromorphic (in the space variable) on the whole complex plane if {epsilon}>1/2, (2) meromorphic on a strip around the real line if {epsilon}=1/2, and (3) Gevrey regular if {epsilon}<1/2. Note that qs need not have any decay or pattern of behavior at -infty.
Series of deformed Camassa-Holm-type equations are constructed using the Lagrangian deformation and Loop algebra splittings. They are weakly integrable in the sense of modified Lax pairs.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا