Nonlocal kinetic equation : integrable hydrodynamic reductions , symmetries and exact solutions
نویسندگان
چکیده
By Gennady A. El†, Anatoly M. Kamchatnov‡, Maxim V. Pavlov z and Sergey A. Zykov § † Department of Mathematical Sciences, Loughborough University, Loughborough, UK ‡Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, Russia z Lebedev Physical Institute, Russian Academy of Sciences, Moscow § SISSA, Trieste, Italy, and Institute of Metal Physics, Urals Division of Russian Academy of Sciences, Ekaterinburg, Russia
منابع مشابه
Kinetic equation for a soliton gas, its hydrodynamic reductions and symmetries
We study a new class of kinetic equations describing nonequilibrium macroscopic dynamics of soliton gases with elastic collisions. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N -component ‘cold-gas’ hydrodynamic reductions. We prove that these reductions represent integrable linearly degener...
متن کاملKinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions
We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N -component ‘cold-gas’ hydrodynamic reductions. We prove that...
متن کاملOn nonlocal structure of the kinetic equation for a soliton gas
We investigate the structure of the nonlocal closure relation in the kinetic equation for a soliton gas. This kinetic equation represents an integro-differential nonlinear system which has been recently shown to possess a number of remarkable properties and seems to be a representative of an entirely new class of integrable systems. In this paper, we identify the nonlocal kinetic closure relati...
متن کاملSelf-similar solutions of certain coupled integrable systems
Similarity reductions of the coupled nonlinear Schrödinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painlevé transcendents, leading to new exact self-similar solutions for these integrable equations. PACS numbers: 02.30.Ik., 02...
متن کاملIntegrable nonlocal nonlinear Schrödinger equation.
A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contras...
متن کامل