The purpose of this work is to find new soliton solutions of the complex Ginzburg–Landau equation(GLE)with Kerr law non-linearity.The considered equation is an imperative nonlinear partial differential equation(PDE)i...The purpose of this work is to find new soliton solutions of the complex Ginzburg–Landau equation(GLE)with Kerr law non-linearity.The considered equation is an imperative nonlinear partial differential equation(PDE)in the field of physics.The applications of complex GLE can be found in optics,plasma and other related fields.The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE.The results are presented under a suitable choice for the values of parameters.Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real,and imaginary parts in order to discuss the similarities and difference between them.The graphical representation of the results depicts the typical behavior of soliton solutions.The obtained soliton solutions are of different forms,such as,hyperbolic and trigonometric functions.The results presented in this paper are novel and reported first time in the literature.Simulation results establish the validity and applicability of the suggested technique for the complex GLE.The suggested method with symbolic computational software such as,Mathematica and Maple,is proven as an effective way to acquire the soliton solutions of nonlinear partial differential equations(PDEs)as well as complex PDEs.展开更多
This paper extracts some analytical solutions of simplified modified Camassa-Holm(SMCH)equations with various derivative operators,namely conformable and M-truncated derivatives that have been recently introduced.The ...This paper extracts some analytical solutions of simplified modified Camassa-Holm(SMCH)equations with various derivative operators,namely conformable and M-truncated derivatives that have been recently introduced.The SMCH equation is used to model the unidirectional propagation of shallowwater waves.The extended rational sine−cosine and sinh−cosh techniques have been successfully implemented to the considered equations and some kinds of the solitons such as kink and singular have been derived.We have checked that all obtained solutions satisfy the main equations by using a computer algebraic system.Furthermore,some 2D and 3D graphical illustrations of the obtained solutions have been presented.The effect of the parameters in the solutions on the wave propagation has been examined and all figures have been interpreted.The derived solutions may contribute to comprehending wave propagation in shallow water.So,the solutions might help further studies in the development of autonomous ships/underwater vehicles and coastal zone management,which are critical topics in the ocean and coastal engineering.展开更多
基金the National Natural Science Foundation of China(Grant Nos.11971142,11871202,61673169,11701176,11626101,11601485).YMC received the grant for this work.
文摘The purpose of this work is to find new soliton solutions of the complex Ginzburg–Landau equation(GLE)with Kerr law non-linearity.The considered equation is an imperative nonlinear partial differential equation(PDE)in the field of physics.The applications of complex GLE can be found in optics,plasma and other related fields.The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE.The results are presented under a suitable choice for the values of parameters.Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real,and imaginary parts in order to discuss the similarities and difference between them.The graphical representation of the results depicts the typical behavior of soliton solutions.The obtained soliton solutions are of different forms,such as,hyperbolic and trigonometric functions.The results presented in this paper are novel and reported first time in the literature.Simulation results establish the validity and applicability of the suggested technique for the complex GLE.The suggested method with symbolic computational software such as,Mathematica and Maple,is proven as an effective way to acquire the soliton solutions of nonlinear partial differential equations(PDEs)as well as complex PDEs.
基金Scientific and Technological Research Council of Turkey(TUBITAK)for the finan-cial support of the 2211-A Fellowship Program.
文摘This paper extracts some analytical solutions of simplified modified Camassa-Holm(SMCH)equations with various derivative operators,namely conformable and M-truncated derivatives that have been recently introduced.The SMCH equation is used to model the unidirectional propagation of shallowwater waves.The extended rational sine−cosine and sinh−cosh techniques have been successfully implemented to the considered equations and some kinds of the solitons such as kink and singular have been derived.We have checked that all obtained solutions satisfy the main equations by using a computer algebraic system.Furthermore,some 2D and 3D graphical illustrations of the obtained solutions have been presented.The effect of the parameters in the solutions on the wave propagation has been examined and all figures have been interpreted.The derived solutions may contribute to comprehending wave propagation in shallow water.So,the solutions might help further studies in the development of autonomous ships/underwater vehicles and coastal zone management,which are critical topics in the ocean and coastal engineering.
