Related papers: Quasi-exact solutions of nonlinear differential eq…
Following a recently introduced approach to approximate Lie symmetries of differential equations which is consistent with the principles of perturbative analysis of differential equations containing small terms, we analyze the case of…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
The objective of this manuscript is to enquire for the solvability of a specific type of non-linear quadratic integral equations via the interesting notion of measure of non-compactness. Firstly, we inquire into couple of exciting fixed…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
In this paper, the problem of approximate symmetries of a class of non-linear reaction-diffusion equations called Kolmogorov-Petrovsky-Piskounov (KPP) equation is comprehensively analyzed. In order to compute the approximate symmetries, we…
We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonlinearities. Furthermore, we provide some applications to…
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New exact solutions of this equation are presented.
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in&…
This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…
In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.
The notion of a noncommutative quasi-resolution is introduced for a noncommutative noetherian algebra with singularities, even for a non-Cohen-Macaulay algebra. If A is a commutative normal Gorenstein domain, then anoncommutative…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
This is a short review of the construction of quasi-periodic (algebraic-geometrical) solutions to hierarchies of nonlinear integrable equations. As is well known, the solutions are expressed through Riemann's theta-functions associated with…
We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas…