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2019•International Journal of Mathematics and Systems ScienceOpen access

The Riccati-Bernoulli Sub-ODE Technique for Solving the Deterministic (Stochastic) Generalized-Zakharov System

Mahmoud A. E. Abdelrahman, Mohamed A. Sohaly

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Abstract

This article concerns with the construction of the analytical traveling wave so- lutions for the Generalized-Zakharov System by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this technique in random case by using random traveling wave trans- formation in order to find what is the effect of the randomness input for this technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique. The first moment of random solution is computed for different statistical probability distributions.

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What this paper is about

This article concerns with the construction of the analytical traveling wave so- lutions for the Generalized-Zakharov System by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this technique in random case by using random traveling wave trans- formation in order to find what is the effect of the randomness input for this technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique. The first moment of random solution is computed for different statistical probability distributions.

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Available abstract

This article concerns with the construction of the analytical traveling wave so- lutions for the Generalized-Zakharov System by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this technique in random case by using random traveling wave trans- formation in order to find what is the effect of the randomness input for this technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique. The first moment of random solution is computed for different statistical probability distributions.

Key concepts: Ode, Bernoulli's principle, Randomness, Mathematics, Riccati equation, Applied mathematics, Bernoulli distribution, Moment (physics)

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