On certain nonlinear evolution equations

Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians

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 ...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Nonlinear Impulsive Evolution Equations

We study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive evolution equation u′(t) = Au(t) + f(t, u(t)), 0 < t < T0, t = ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, ..., 0 < t1 < t2 < ... < T0, in a Banach space X, where A is the generator of a strongly continuous semigroup, ∆u(ti) = u(t+i ) − u(ti ), and Ii’s are some operators. The impulsive conditions c...