Diffusion-Reaction (DR) equation has been used to model a large number of phenomena in nature. It may be mentioned that a linear diffusion equation does not exhibit any traveling wave solution. But there are a vast nu...Diffusion-Reaction (DR) equation has been used to model a large number of phenomena in nature. It may be mentioned that a linear diffusion equation does not exhibit any traveling wave solution. But there are a vast number of phenomena in different branches not only of science but also of social sciences where diffusion plays an important role and the underlying dynamical system exhibits traveling wave features. In contrast to the simple diffusion when the reaction kinetics is combined with diffusion, traveling waves of chemical concentration are found to exist. This can affect a biochemical change, very much faster than straight diffusional processes. This kind of coupling results into a nonlinear (NL) DR equation. In recent years, memory effect in DR equation has been found to play an important role in many branches of science. The effect of memory enters into the dynamics of NL DR equation through its influence on the speed of the travelling wavefront. In the present work, chemotaxis equation with source term is studied in the presence of finite memory and its solution is compared with the corresponding chemotaxis equation without finite memory. Also, a comparison is made between Fisher-Burger equation and chemotaxis equation in the presence of finite memory. We have shown that nonlinear diffusion-reaction-convection equation is equivalent to chemotaxis equation.展开更多
Non-canonical Lagrangian (Lagrangian with non-quadratic kinetic term) has been studied in the context of cosmology. In this work, the non-canonical Lagrangian with potential energy term has been discussed. We have obt...Non-canonical Lagrangian (Lagrangian with non-quadratic kinetic term) has been studied in the context of cosmology. In this work, the non-canonical Lagrangian with potential energy term has been discussed. We have obtained the periodic and solitary wave solutions for certain types of potential. The solutions obtained here may provide some new direction in the theory of phase transition, quantum field theory and related phenomena.展开更多
文摘Diffusion-Reaction (DR) equation has been used to model a large number of phenomena in nature. It may be mentioned that a linear diffusion equation does not exhibit any traveling wave solution. But there are a vast number of phenomena in different branches not only of science but also of social sciences where diffusion plays an important role and the underlying dynamical system exhibits traveling wave features. In contrast to the simple diffusion when the reaction kinetics is combined with diffusion, traveling waves of chemical concentration are found to exist. This can affect a biochemical change, very much faster than straight diffusional processes. This kind of coupling results into a nonlinear (NL) DR equation. In recent years, memory effect in DR equation has been found to play an important role in many branches of science. The effect of memory enters into the dynamics of NL DR equation through its influence on the speed of the travelling wavefront. In the present work, chemotaxis equation with source term is studied in the presence of finite memory and its solution is compared with the corresponding chemotaxis equation without finite memory. Also, a comparison is made between Fisher-Burger equation and chemotaxis equation in the presence of finite memory. We have shown that nonlinear diffusion-reaction-convection equation is equivalent to chemotaxis equation.
文摘Non-canonical Lagrangian (Lagrangian with non-quadratic kinetic term) has been studied in the context of cosmology. In this work, the non-canonical Lagrangian with potential energy term has been discussed. We have obtained the periodic and solitary wave solutions for certain types of potential. The solutions obtained here may provide some new direction in the theory of phase transition, quantum field theory and related phenomena.
