ترغب بنشر مسار تعليمي؟ اضغط هنا

Nearly linear dynamics of nonlinear dispersive waves

129   0   0.0 ( 0 )
 نشر من قبل Vadim Zharnitsky Vadim Zharnitsky
 تاريخ النشر 2010
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.



قيم البحث

اقرأ أيضاً

355 - Masaya Maeda , Akito Suzuki 2019
In this paper, we consider the continuous limit of a nonlinear quantum walk (NLQW) that incorporates a linear quantum walk as a special case. In particular, we rigorously prove that the walker (solution) of the NLQW on a lattice $delta mathbb Z$ unif ormly converges (in Sobolev space $H^s$) to the solution to a nonlinear Dirac equation (NLD) on a fixed time interval as $deltato 0$. Here, to compare the walker defined on $deltamathbb Z$ and the solution to the NLD defined on $mathbb R$, we use Shannon interpolation.
The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring in other layers of the current does not affect the wave motion. The equations of motion are formulated as a Hamiltonian system.
We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3beta-1} V (N^beta x)$, for an arbitrary parameter $beta in (0,1)$. We provide a norm-approximation for the many-body evolut ion of initial data exhibiting Bose-Einstein condensation in terms of a cubic nonlinear Schrodinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations.
152 - Zhiwu Lin 2008
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain criteria for the existence of exponentially growing solutions to the linearized problem. The novelty is that we dealt with models with nonlocal dispersive terms, for which the spectra problem is out of reach by the Evans function technique. For the proof, we reduce the linearized problem to study a family of nonlocal operators, which are closely related to properties of solitary waves. A continuation argument with a moving kernel formula are used to find the instability criteria. Recently, these techniques have also been extended to study instability of periodic waves and to the full water wave problem.
187 - Maram Akila , Boris Gutkin 2015
The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian Unitary Ensemble. These degeneracies, however, are lifted when the unidirect ionality is broken in one of the graphs vertices by a singular perturbation. Based on a Random Matrix model we derive an analytic expression for the nearest neighbour distribution between energy levels of such systems. As we demonstrate the result agrees excellently with the actual statistics for graphs with a uniform distribution of eigenfunctions. Yet, it exhibits quite substantial deviations for classes of graphs which show strong scarring.
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