In many fields of physics and chemistry, explicit analytical solutions of the fundamental dynamical equations are much valuable for a general understanding of phenomena, e. g. the role played by physical parameters. Two typical examples in quantum mechanics are the exact solutions of the Schrödinger equation (SE) for a hydrogen atom (Coulombic) and for a harmonic oscillator [1 – 3]. The Mie-typ...

in this article, the modified exp-function method is used to construct many exact solutions to the nonlineargeneralized k(n,n) and bbm equations with variable coefficients. under different parameter conditions, explicitformulas for some new exact solutions are successfully obtained. the proposed solutions are found to beimportant for the explanation of some practical physical problems.

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...

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For a Hertz chain model, by using the methodology of dynamical systems and singular traveling wave theory developed Li Chen [9] to its system defined on two-dimensional foliations in three-dimensional space, under different parameter conditions, existence all possible bounded solutions (solitary solutions, periodic peakons, compactons) is proved. nonlinearity exponent $ k = \frac32, 2 3 as many...

The problem of controlling a compound Poisson process until it leaves an interval is considered. This type known as homing problem. To determine the value optimal control, we must solve nonlinear integro-differential equation. Exact and explicit solutions are obtained for two possible jumps size distributions.

we present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with lr fuzzy variables. as solutions, notions of exact and approximate solutions are considered. we transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. if the corresponding crisp system is incompatible, then the fuzzy ...

in this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (fpdes) in the sense of modified riemann-liouville derivative. with the aid of symbolic computation, we choose the space-time fractional zakharov-kuznetsov-benjamin-bona-mahony (zkbbm) equation in mathematical physics with a source to illustrate the validity a...