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- M Lakshmanan, R Myrzakulov, S Vijayalakshmi, A K Danlybaeva
- 1998

It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a… (More)

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals of motion associated with the given equation so that the general solution follows straightforwardly from these integrals. The method is illustrated with… (More)

- R Gopal, V K Chandrasekar, A Venkatesan, M Lakshmanan
- Physical review. E, Statistical, nonlinear, and…
- 2014

By developing the concepts of strength of incoherence and discontinuity measure, we show that a distinct quantitative characterization of chimera and multichimera states which occur in networks of coupled nonlinear dynamical systems admitting nonlocal interactions of finite radius can be made. These measures also clearly distinguish between chimera or… (More)

- T Kanna, M Lakshmanan
- Physical review letters
- 2001

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schrödinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general N-coupled nonlinear Schrödinger equations ( N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to… (More)

A method of finding general solutions of second-order nonlinear ordinary differential equations by extending the Prelle-Singer (PS) method is briefly discussed. We explore integrating factors, integrals of motion and the general solution associated with several dynamical systems discussed in the current literature by employing our modifications and… (More)

By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrödinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision properties, which have not been observed in any other (1+1) dimensional soliton system so far. In particular, we identify… (More)

- M. Lakshmanan
- 1998

Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schrödinger equation (NLSE) originally discovered by Calogero, discussed then by Zakharov and recently rederived by Strachan, have been estabilished. A compatible set of three linear… (More)

Coupled second order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential equations we focus our attention on the method of deriving general solution of two coupled second order nonlinear ordinary differential equations through the… (More)

- R Radhakrishnan, A Kundu, M Lakshmanan
- Physical review. E, Statistical physics, plasmas…
- 1999

We propose an integrable system of coupled nonlinear Schrödinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in non-Kerr media. Lax pairs, conserved quantities and exact soliton solutions for the proposed integrable model are given. The explicit form of two solitons… (More)

- D V Senthilkumar, M Lakshmanan
- Physical review. E, Statistical, nonlinear, and…
- 2005

The existence of anticipatory, complete, and lag synchronization in a single system having two different time delays, that is, feedback delay tau1 and coupling delay tau2, is identified. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay tau2 with a suitable stability… (More)