Abstract
Using the extended F‐expansion method based on computerized symbolic computation technique, we find several new solutions of (1+1)‐dimensional and (2+1)‐dimensional Ito equations. These solutions contain hyperbolic and triangular solutions. It is shown that the power of the extended F‐expansion method is its ease of use to determine shock or solitary type of solutions. In addition, as an illustrative sample, the properties for the extended F‐expansion solutions of the Ito equations are shown with some figures.
Highlights
The nonlinear wave phenomena can be observed in various scientific fields, such as plasma physics, optical fibers, fluid dynamics, and chemical physics
It is shown that soliton solutions and triangular periodic solutions can be established as the limits of Jacobi doubly periodic wave solutions
When m → 1. the Jacobi functions degenerate to the hyperbolic functions, that is, snζ → tanh ζ, cnζ → sechζ, dnζ → sechζ, 2.9
Summary
The nonlinear wave phenomena can be observed in various scientific fields, such as plasma physics, optical fibers, fluid dynamics, and chemical physics. The nonlinear wave phenomena can be obtained in solutions of nonlinear evolution equations NEEs. The study of NLEEs appear everywhere in applied mathematics and theoretical physics including engineering sciences and biological sciences. Porubov et al 27–29 have obtained some exact periodic solutions to some nonlinear wave equations, they use the Weierstrass elliptic function and involve complicated deducing. A Jacobi elliptic function JEF expansion method, which is straightforward and effective, was proposed for constructing periodic wave solutions for some nonlinear evolution equations. The Jacobi periodic solution in terms of sn may be obtained by applying the sn-function expansion. We extend the EFE method with symbolic computation to 1.1 and 1.2 for constructing their interesting Jacobi doubly periodic wave solutions. The algorithm that we use here is a computerized method, in which we are generating an algebraic system
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