In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special param...In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special parameter where satisfies a second order linear differential equation , , where and are functions of .展开更多
The new generalized (G'/G)-expansion method is one of the powerful and competent methods that appear in recent time for establishing exact solutions to nonlinear evolution equations (NLEEs). We apply the new gener...The new generalized (G'/G)-expansion method is one of the powerful and competent methods that appear in recent time for establishing exact solutions to nonlinear evolution equations (NLEEs). We apply the new generalized (G'/G)-expansion method to solve exact solutions of the new coupled Konno-Oono equation and construct exact solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. The significance of obtained solutions gives credence to the explanation and understanding of related physical phenomena. As a newly developed mathematical tool, this method efficiency for finding exact solutions has been demonstrated through showing its straightforward nature and establishing its ability to handle nonlinearities prototyped by the NLEEs whether in applied mathematics, physics, or engineering contexts.展开更多
In this paper,we used the generalized(G’/G)-expansion method to construct exact solutions for conformable fractional nonlinear partial differential equations.This method is applied to obtain exact solutions for confo...In this paper,we used the generalized(G’/G)-expansion method to construct exact solutions for conformable fractional nonlinear partial differential equations.This method is applied to obtain exact solutions for conformable fractional equal width wave equation(EW equation)and conformable fractional modified equal width wave equation(MEW equation).Based on the proposed method,several new exact solutions have been obtained.The proposed method is powerful and easily applicable for solving different types of conformable fractional partial differential equations.展开更多
The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments...The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments show exactly that rogue waves occur in deep and shallow water. To study the behavior of freak waves in terms of their space and time evolution, that is, their motion and also in terms of mechanical transformations that these systems may suffer in their dealings with other systems, we derive a modified nonlinear Schrödinger equation modeling the propagation of rogue waves in deep water in order to seek analytic solutions of this nonlinear partial differential equation by using generalized extended G'/G-expansion method with the aid of mathematica. Particular attentions have been paid to the behavior of rogue wave’s amplitude which highlights rogue wave’s destructive power.展开更多
文摘In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special parameter where satisfies a second order linear differential equation , , where and are functions of .
基金The Special Foundation of Doctoral Unit of the Ministry of Education of China(No.20070128001)Scientific Research Innovation Project of Shanghai Education Committee(No.09YZ239)Scientific Research Foundation of Inner Mongolia University of Technology(No.ZS201033)~~
文摘The new generalized (G'/G)-expansion method is one of the powerful and competent methods that appear in recent time for establishing exact solutions to nonlinear evolution equations (NLEEs). We apply the new generalized (G'/G)-expansion method to solve exact solutions of the new coupled Konno-Oono equation and construct exact solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. The significance of obtained solutions gives credence to the explanation and understanding of related physical phenomena. As a newly developed mathematical tool, this method efficiency for finding exact solutions has been demonstrated through showing its straightforward nature and establishing its ability to handle nonlinearities prototyped by the NLEEs whether in applied mathematics, physics, or engineering contexts.
文摘In this paper,we used the generalized(G’/G)-expansion method to construct exact solutions for conformable fractional nonlinear partial differential equations.This method is applied to obtain exact solutions for conformable fractional equal width wave equation(EW equation)and conformable fractional modified equal width wave equation(MEW equation).Based on the proposed method,several new exact solutions have been obtained.The proposed method is powerful and easily applicable for solving different types of conformable fractional partial differential equations.
文摘The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments show exactly that rogue waves occur in deep and shallow water. To study the behavior of freak waves in terms of their space and time evolution, that is, their motion and also in terms of mechanical transformations that these systems may suffer in their dealings with other systems, we derive a modified nonlinear Schrödinger equation modeling the propagation of rogue waves in deep water in order to seek analytic solutions of this nonlinear partial differential equation by using generalized extended G'/G-expansion method with the aid of mathematica. Particular attentions have been paid to the behavior of rogue wave’s amplitude which highlights rogue wave’s destructive power.
基金Supported by the Special Foundation of Doctoral Unit of the Ministry of Education of China(No.20070128001)Scientific Research innovation Project of Shanghai Education Committee(No.09YZ239)~~
