Linear differential equations to solve nonlinear mechanical problems: A novel approach

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Nair, C. Radhakrishnan (2004)
  • Subject: Nonlinear Sciences - Chaotic Dynamics

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differential equations are put into non-linear differential equations and checked whether these solutions are also solutions of the original non-linear differential equation. It is found that many solutions of the linear differential equations are also solutions of the original non-linear differential equation.
  • References (7)

    [2] John DW and Smith P (1986) Nonlinear Ordinary Differential Equations, 2nd edn, (Oxford: Clarendon Press).

    [3] Dodd RK, Eilbeck JC, Gibben JD (1984) Solitons and Nonlinear Wave Equation, (New York: Academic).

    [4] Batchelor GK (1993) An Introduction to Fluid dynamics. 1st Indian edn, (New Delhi) PP 147.

    [5] Rajaram R (1982) Solitons and Instantons 1st edn, (New Delhi).

    [6] Michael Tabor (1989) Chaos and Integrability in Nonlinear Dynamics-An Introduction, (New York: John Wiley and Sons).

    [7] Ronald Adler, Maurice Bazin, Menahem Schiffer (1975) Introduction to General Relativity, 2nd edn, (Kogakuzha, Tokyo: McGraw-Hill).

    [8] Drazin PG and Johnson RS (1990) Solitons: An Introduction. (Cambridge: Cambridge University Press).

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