Searching for Analytical Solutions of the (2+1)‐Dimensional KP Equation by Two Different Systematic Methods

Abstract

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

“…In recent years, many mathematicians and physicists studied the nonlinear integrable systems that occur in various fields such as biology, fluid dynamics, quantum and plasma physics, thermal engineering and optics. Plenty of methods have been developed for getting exact solutions to nonlinear differential equations such as the modified extended tanh method [1,2], the improved F-expansion method [3], the modified simple equation method [4], the complex method [5][6][7][8], the generalized ( ′/ ) G G -expansion method [9][10][11], the exp(− ( )) ψ z -expansion method [12][13][14][15][16], the ( + / ′) m G 1 -expansion method [17], the sine-Gordon expansion method [18][19][20][21][22][23][24], the extended sine-Gordon expansion method [25][26][27], the extended rational sinh-cosh method [28], the modified Kudryashov method [29] and other methods [30][31][32].…”

Study on the Design of Cantonese Cultural and Creative Products using Analytic Hierarchy Process

“…In the research of social science [11] and natural science [12][13][14][15][16][17][18], the selection of methods is very important. In this paper, we choose to use an effective method, AHP, to study the design of Cantonese cultural and creative products.…”

Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method

“…In present work, our goal is to solve the nonlinear fractional Liouville equation by using the extended complex method based on the work of Yuan et al [38][39][40][41][42][43]. This is a beneficial technique to attain exact analytical solutions.…”