We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.

The conservation laws for the integrable coupled KDV type system, complexly coupled kdv system, coupled system arising from complex-valued KDV in magnetized plasma, Ito integrable system, and Navier stokes equations of gas dynamics are computed by multipliers approach. First of all, we calculate the multipliers depending on dependent variables, independent variables, and derivatives of dependen...

In this article, we use the homotopy perturbation transform method to find fractional Kersten–Krasil’shchik coupled Korteweg–de Vries (KdV) non-linear system. This system is typically used describe electric circuits, traffic flow, shallow water waves, elastic media, electrodynamics, etc. The modified with help of ρ-Laplace transformation investigate solution given examples show accuracy current...

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long WaveBurgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational for...

the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

Novel explicit rogue wave solutions of the coupled Hirota equations are obtained by using the Darboux transformation. In contrast to the fundamental Peregrine solitons and dark rogue waves, we present an interesting rogue-wave pair that involves four zero-amplitude holes for the coupled Hirota equations. It is significant that the corresponding expressions of the rogue-wave pair solutions conta...

In this paper, a simplified bilinear method combined with a fractional transform has been used to obtain a new multiple soliton solutions for the Fractional coupled fractional kdV equations with variable coefficients. These systems appear in biology, engineering, mechanics, complex physics phenomena economics, signal image processing, notably control theory, groundwater problems and chemistry. ...

<p style='text-indent:20px;'>Inspired by the recent successful completion of study well-posedness theory for Cauchy problem Korteweg-de Vries (KdV) equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_t +uu_x +u_{xxx} = 0, \quad \left. u \right |_{t 0} u_{0} $\end{document} </tex-math></disp-formula...

this paper addresses synchronizing two coupled chaotic fitzhugh–nagumo (fhn) neurons with weakly gap junction under external electrical stimulation (ees). to transmit information among coupled neurons, by generalization of the integer-order fhn equations of the coupled system into the fractional-order in frequency domain using crone approach, the behavior of each coupled neuron relies on its pa...

The lattice Gelfand-Dickey hierarchy is a version of the hierarchy. A special case KdV Inspired by recent work Buryak and Rossi, we propose an extension extended system has infinite number logarithmic flows alongside usual flows. We present Lax, Sato Hirota equations factorization problem difference operators that captures whole set solutions. construction this resembles 1D bigraded Toda hierar...