International Journal of Mathematics and Mathematical Sciences, 1995 In this paper, we study initial value problems for coupld second order delay differential equations with variable coefficients. By means of the application of the method of steps and the method of Frobenius, the exact solution of the problem is ...
R. J. Villanueva +2 more
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Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method [PDF]
, 2010 The homotopy analysis method is applied to the Degasperis-Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves.
Abbasbandy, S., Parkes, E.J.
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A methodological approach to solving the Korteweg–de Vries equation in its various forms
Scientific AfricanThe Korteweg-de Vries (KdV) equation, an evolution-type nonlinear partial differential equation (PDE), describes the propagation of solitary water waves as observed in the literature.
Francis Tuffour +3 more
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New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation
Nonlinear Engineering, 2021 In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to
Inc Mustafa +5 more
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Exact Closed-Form Solution for the Oscillator with a New Type of Mixed Nonlinear Restitution Force
Mathematics, 2023 This paper shows an oscillator with a spring made of material where the stress is a function not only of strain but also strain rate. The corresponding restitution force is of strong nonlinear monomial type and is the product of displacement and velocity
Livija Cveticanin
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Quantum decay model with exact explicit analytical solution [PDF]
Physical Review A, 2009 4 pages, 3 ...
Marchewka, Avi, Granot, Er'el
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Growth index with the exact analytic solution of sub-horizon scale linear perturbation for dark energy models with constant equation of state [PDF]
, 2010 Three decades ago Heath found the integral form of the exact analytic growing mode solution of the linear density perturbation δ on sub-horizon scales including the cosmological constant or the curvature term.
Lee, Seokcheon, Ng, Kin-Wang
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Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method
Journal of Applied Mathematics, 2012 The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series ...
Mojtaba Nazari +3 more
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Accelerated HPSTM: An efficient semi-analytical technique for the solution of nonlinear PDE’s
Nonlinear Engineering, 2020 In this paper a novel technique i.e. accelerated homotopy perturbation Sumudu transformation method (AHPSTM), which is a hybrid of accelerated homotopy perturbation method and Sumudu transformation to obtain an approximate analytic solution of nonlinear ...
Grover Deepak +2 more
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Exact analytical solutions of second order conformal hydrodynamics [PDF]
Physical Review D, 2014 We present some exact solutions of relativistic second-order hydrodynamic equations in theories with conformal symmetry. Starting from a spherically expanding solution in ideal hydrodynamics, we take into account general conformal second-order corrections, and construct, for the first time, fully analytical axisymmetric exact solutions including the ...
Hatta, Yoshitaka +2 more
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