Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
نویسندگان
چکیده
Algebraic geometrical solutions of a new shallow-water equation and Dymtype equation are studied in connection with Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobians. These equations belong to a class of N -component integrable systems generated by Lax equations with energydependent Schrödinger operators having poles in the spectral parameter. The classes of quasi-periodic and soliton-type solutions of these equations are described in terms of thetaand tau-functions by using new parametrizations. A qualitative description of real-valued solutions is provided.
منابع مشابه
Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
The algebraic–geometric approach is extended to study evolution equations associated with the energy-dependent Schrödinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvarieties of Jacobi varieties. The general approach is demonstrated by using new parametrizations for constructing quasi-periodic solutions of the shallow-...
متن کاملA Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کاملThe B"{a}cklund transformation method of Riccati equation to coupled Higgs field and Hamiltonian amplitude equations
In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...
متن کاملStochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کامل0 On billiard weak solutions of nonlinear PDE ’ s and Toda flows ∗
A certain class of partial differential equations possesses singular solutions having discontinuous first derivatives (“peakons”). The time evolution of peaks of such solutions is governed by a finite dimensional completely integrable system. Explicit solutions of this system are constructed by using algebraic-geometric method which casts it as a flow on an appropriate Riemann surface and reduc...
متن کامل