In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

The recently developed Lindblad approach for quantum dynamics of an open system with linear dissipation has been extended to a model of nonlinear coupling. The coupling term Hi5(kCk f (x)qk is an arbitrary function of the system coordinate, but remains to be linear in bath coordinates. A Lindblad master equation and its associated stochastic differential equation have been obtained. To study di...

A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.

Many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on Duffing equation. Analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. In this paper, the general form of Duffing equation with cubic nonlinearity as well as par...

Direct Simulation Monte Carlo (DSMC) is a particle-based simulation method for gas dynamics. The method can be viewed as either a simplified molecular dynamics (DSMC being several orders of magnitude faster) or as a Monte Carlo method for solving the time-dependent nonlinear Boltzmann equation. The DSMC method has been used successfully in the study of rarefied gas flows for several decades but...

We undertake a detailed comparison of the results of direct numerical simulations of the soliton gas dynamics for the Korteweg – de Vries equation with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. Two model problems are considered: (i) the propagation of a ‘trial’ soliton through a one-component ‘cold’ soliton gas consisting of rand...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a q-Gaussian trial wave-function that interpolates between the low-and the high-density limit of the ground state of a Bose-condensed gas. Our main result consists of reducing the Gross-Pitaevskii equation, a nonlinear partial ...

in this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. this controller is derived based on the closed form solution of the hamilton-jacobi-bellman (hjb) equation associated with the cheap control problem. this methodology employs an algebraic equation with parametric coefficients for the systems with s...