Exact solutions to conformable time fractional (3+1)dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebrai...

This paper studies the generalized version of the ZakharovKuznetsov Benjamin-Bona-Mahoney equation. The functional variable method as well as the simplest equation method are applied to obtain solitons and singular periodic solutions to the equation. There are several constraint conditions that are naturally revealed in order for these specialized type of solutions to exist. The results of this...

A family of local spectral evolution kernels (LSEKs) are derived for analytically integrating a class of partial differential equations (PDEs) 0021-9 doi:10. * Co E-m o ot u 1⁄4 AðtÞ o 2 ox2 þ BðtÞ o ox þ CðtÞ u: The LSEK can solve the above PDEs with x-independent coefficients in a single step. They are utilized in operator splitting schemes to arrive at a local spectral time-splitting (LSTS) ...

In this paper we introduce and examine a generalization of the complex Ginzburg-Landau equation (CGLE) where the self-interaction contained in the cubic term is replaced by a coupling involving the original field and a low-frequency one. New instabilities arise and a radically new asymptotic dynamical behavior emerges displaying defect turbulence over wide regions of the parameter space.

We present two numerical methods for the approximation of the generalized Zakharov system (ZS). The first one is the time-splitting spectral (TSSP) method, which is explicit, time reversible, and time transverse invariant if the generalized ZS is, keeps the same decay rate of the wave energy as that in the generalized ZS, gives exact results for the plane-wave solution, and is of spectral-order...

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schrödinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of sc...

Exact solutions of differential equations of physics are very important for the understanding of various physical phenomena. The generation and application of new methods of calculation of exact solutions was and is actual task in all times for human scientific civilization. In the last two decades the Inverse Spectral Transform (IST) method has been generalized and successfully applied to vari...