Solitary and Self-similar Solutions of Two-component System of Nonlinear Schrödinger Equations
نویسندگان
چکیده
Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrödinger equations (NLSE). Here we consider simultaneous blow-up solutions of two-component system of self-focusing NLSE. By studying the associated self-similar solutions, we prove two components of solutions blow up at the same time. These self-similar solutions may come from solitary wave solutions with multi-bumps forming abundant geometric patterns which cannot be found in one-component self-focusing NLSE. Our results may provide the first step to investigate optical turbulence in two-component system of NLSE.
منابع مشابه
Self-similar and Solitary Wave Solutions with Ring Profiles of Two-component Nonlinear Schrödinger Systems
Blowup ring profiles have been investigated by finding self-similar non-vortex solutions of nonlinear Schrödinger equations (NLSE) (cf. [4] and [5]). However, those solutions have infinite L norm so one may not maintain the ring profile all the way up to the singularity. To find selfsimilar H non-vortex solutions with ring profiles, we study self-similar solutions of two-component systems of NL...
متن کاملSymbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrödinger Equations
Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when selfinteraction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrödinger equations with repulsive self-interacti...
متن کاملConstuction of solitary solutions for nonlinear differential-difference equations via Adomain decomposition method
Here, Adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear differential difference equation and Relativistic Toda couplednonlinear differential-difference equation are chosen to illustrate the validity andthe g...
متن کاملStability in H 1 of the Sum of K Solitary Waves for Some Nonlinear Schrödinger Equations
In this article we consider nonlinear Schrödinger (NLS) equations in R for d = 1, 2, and 3. We consider nonlinearities satisfying a flatness condition at zero and such that solitary waves are stable. Let Rk(t, x) be K solitary wave solutions of the equation with different speeds v1, v2, . . . , vK . Provided that the relative speeds of the solitary waves vk − vk−1 are large enough and that no i...
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کامل