Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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68 citations
TL;DR: In this paper, an improved tanh function method is used with a computerized symbolic computation for constructing new exact travelling wave solutions on two nonlinear physical models namely, the quantum Zakharov equations and the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system.
Abstract: In this paper, an improved tanh function method is used with a computerized symbolic computation for constructing new exact travelling wave solutions on two nonlinear physical models namely, the quantum Zakharov equations and the (2+1)-dimensional Broer–Kaup–Kupershmidt (BKK) system. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions.The exact solutions are obtained which include new soliton-like solutions, trigonometric function solutions and rational solutions. The method is straightforward and concise, and its applications are promising.
67 citations
TL;DR: In this article, the nonlinear Schrodinger equation is derived in a general intrinsic geometric setting involving a normal congruence originally investigated by Marris and Passman in 1969 in a hydrodynamical context.
Abstract: The nonlinear Schrodinger equation is derived in a general intrinsic geometric setting involving a normal congruence originally investigated by Marris and Passman in 1969 in a hydrodynamical context. Geometric properties of members of the normal congruence are adduced and an intrinsic representation of the auto-Backlund transformation is obtained for the nonlinear Schrodinger equation.
67 citations
TL;DR: In this paper, the authors study the oscillation of first-order delay equations using a method that parallels the use of Riccati equations in the study of second-order ordinary differential equations without delay.
67 citations
TL;DR: In this article, the basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed, and the relation of this last theory with a generalization of the classical Factorization Method presented by Infeld and Hull is analyzed in detail.
Abstract: The basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a generalization of the classical Factorization Method presented by Infeld and Hull is analyzed in detail. By the use of some properties of the Riccati equation the solutions of Infeld and Hull are generalized in a simple way.
67 citations