Traveling wave solutions for complex nonlinear space–time fractional order (2 + 1)-dimensional Maccari dynamical system and Schrödinger equation with dual power law nonlinearity

Abstract

The traveling wave solutions for complex (2 + 1)-dimensional Maccari dynamical system and Schrödinger equation in both space and time fractional terms are studied in this paper. Using extended simple equation method, exact, periodic and soliton solutions in fractional form are extracted for both models under study confirming the effectiveness of the method. The obtained fractional results have a variety of applications in fibre optics, quantum mechanics, oceanic and optical sciences.

Exact solutions of $$(3+1)$$-dimensional fractional mKdV equations in conformable form via $$\exp (-\phi (\tau ))$$ expansion method

“…Some of these methods are: The ansatz [15,16], the modified simple equation [17,18], the extended trial equation [19], the G ′ G -expansion [20,21], the sine-Gordon expansion [22,23]. Additionally, some other work like a modified form of Kudryashov and functional variable methods [24][25][26] have been done by several scholars in [27,28]. In [29][30][31][32][33][34], the auxiliary equation, the extended tanh-function, the improved tan ( ) 2 -expansion method and the exp function methods have been investigated for difference and fractional order PDEs as well.…”

Studying the periodic solitary, rational solitary and solitary waves of the nonlinear (2+1)-dimensional Maccari couple model in water wave dynamics

“…Many effective and promising techniques to solving NLPDMs have been found, and there has been significant development in the literature in exploring the closed form wave solutions to NLPDMs . Inspired by the various techniques employed in the literature, we applied the new ansatz transformation of the Riccati equation rational expansion method (REREM) [29] to study the analytical solution of the nonlinear (2+1)-dimensional Maccari couple model (MCM) [30,31], that states as:…”

“…From the Kadomstev-Petviashvili equation, Maccari created the (2+1)-dimensional MCM using the asymptotically exact reduction technique, which involves a Fourier expansion and dynamical rescaling [31]. The Maccari model, which is widely used in marine and optical studies, represents erratic waves in water wave dynamics.…”

“…The Maccari model, which is widely used in marine and optical studies, represents erratic waves in water wave dynamics. By various methods, a number of solutions to the Maccari model have been extracted [30,31]. Nonetheless, the implementation of the new modified ansatz transformation on RERM to discover the analytical Maccari model solution is rarely researched.…”