اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA new integrable model of long wave-short wave interaction and linear stability spectra
170
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider the propagation of short waves which generate waves of much longer (infinite) wave-length. Model equations of such long wave-short wave resonant interaction, including integrable ones, are well-known and have received much attention because of their appearance in various physical contexts, particularly fluid dynamics and plasma physics. Here we introduce a new long wave-short wave integrable model which generalises those first proposed by Yajima-Oikawa and by Newell. By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearised long wave-short wave model equations. The geometrical features of this spectrum are related to the stability/instability properties of the solution under scrutiny. Stability spectra for the plane wave solutions are fully classified in the parameter space together with types of modulational instabilities.
قيم البحث
اقرأ أيضاً
We classify 2+1 dimensional integrable systems with nonlocality of the intermediate long wave type. Links to the 2+1 dimensional waterbag system are established. Dimensional reductions of integrable systems constructed in this paper provide dispers
ive regularisations of hydrodynamic equations governing propagation of long nonlinear waves in a shear flow with piecewise linear velocity profile (for special values of vorticities).
We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long-wave in
two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painleve analysis. Then we construct the exact bright multi-soliton solutions by applying the Hirotas bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.
We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integra
ble system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.
We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase trans
ition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.
In classical shallow water wave (SWW) theory, there exist two integrable one-dimensional SWW equation [Hirota-Satsuma (HS) type and Ablowitz-Kaup-Newell-Segur (AKNS) type] in the Boussinesq approximation. In this paper, we mainly focus on the integra
ble SWW equation of AKNS type. The nonlocal symmetry in form of square spectral function is derived starting from its Lax pair. Infinitely many nonlocal symmetries are presented by introducing the arbitrary spectrum parameter. These nonlocal symmetries can be localized and the SWW equation is extended to enlarged system with auxiliary dependent variables. Then Darboux transformation for the prolonged system is found by solving the initial value problem. Similarity reductions related to the nonlocal symmetry and explicit group invariant solutions are obtained. It is shown that the soliton-cnoidal wave interaction solution, which represents soliton lying on a cnoidal periodic wave background, can be obtained analytically. Interesting characteristics of the interaction solution between soliton and cnoidal periodic wave are displayed graphically.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
