First Integral Method for Constructing New Exact Solutions of The important Nonlinear Evolution Equations in Physics

Exact solutions of nonlinear interval Volterra integral equations

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.

New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

and Applied Analysis 3 P(X, Y) = ∑ m i=0 a i (X)Y i is an irreducible polynomial in the complex domain C[X, Y] such that P [X (ξ) , Y (ξ)] = m ∑ i=0 a i (X (ξ)) Y i (ξ) = 0, (13) where a i (X), (i = 0, 1, 2, . . . , m) are polynomials of X and a m (X) ̸ = 0. Equation (13) is called the first integral to (12a) and (12b). Due to the Division Theorem, there exists a polynomial h(X) + g(X)Y in the c...

Constructing new periodic exact solutions of evolution equations.

For the nonlinear Schrödinger equation, the Korteweg-de Vries equation, and the modified Korteweg-de Vries equation, periodic exact solutions are constructed from their stationary periodic solutions, by means of the Bäcklund transformation. These periodic solutions were not written down explicitly before to our knowledge. Their asymptotic behavior when t-->-infinity is different from that when ...

exact solutions of nonlinear interval volterra integral equations