International Journal of Mathematical Analysis and Applications International Journal of Mathematical Analysis and Applications International Journal of Mathematical Analysis and Applications International Journal of Mathematical Analysis and Applications 2014; 1(1): 9-19 Published online March 10, 2014 (http://www.aascit.org/journal/ijmaa) Keywords Exact Solution, Kadomtsev-Petviashvili Equation, Extended Tan-Cot Method, Nonlinear Partial Differential Equations Received: February 11, 2014 Revised: February 20, 2014 Accepted: February 21, 2014 Extended tan-cot method for the solitons solutions to the (3+1)-dimensional Kadomtsev-Petviashvili equation Anwar Ja'afar Mohamad Jawad Al-Rafidain University College , Baghdad, Iraq Email address anwar_jawad2001@yahoo.com Citation Anwar Ja'afar Mohamad Jawad. Extended tan-Cot Method for the Solitons Solutions to the (3+1)-Dimensional Kadomtsev-Petviashvili Equation. International Journal of Mathematical Analysis and Applications. Vol. 1, No. 1, 2014, pp. 9-19. Abstract The proposed extended tan-cot method is applied to obtain new exact travelling wave solutions to the (3+1)-dimensional Kadomtsev-Petviashvili equation and (2+1)- dimensional equation. The method is applicable to a large variety of nonlinear partial differential equations. The tan-cot method seems to be powerful tool in dealing with nonlinear physical models. 1. Introduction Solitons are found in many physical phenomena. Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. Solitons are solitary waves with elastic scattering property. Due to dynamical balance between the nonlinear and dispersive effects these waves retain their shapes and speed to a stable waveform after colliding with each other. Onebasic expression of a solitary wave solution is of the form[1]: ) ( ) , ( t x f t x u λ - = (1) where λ is the speed of wave propagation. For 0 > λ , the wave moves in the positive x direction, whereas the wave moves in the negative x direction for 0 < λ . Travelling waves, whether their solution expressions are in explicit or implicit forms are very interesting from the point of view of applications. These types of waves will not change their shapes during propagation and are thus easy to detect. Of particular interest are three types of travelling waves: the solitary waves, which are localized travelling waves, asymptotically zero at large distances, the periodic waves, which rise or descend from one asymptotic state to another. Recently, algebraic method, called the mapping method [2], is proposed to obtain exact travelling wave solutions for a large variety of nonlinear partial differential equations (PDEs). Other methods are proposed to obtain exact travelling wave solutions such as sine-cosine-function method[3], tanh-coth method[4-5], tan-cot- function method [6-7], sech method [8].