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Now we apply the multiple scales technique [34] to treat Eqs.
A multiple scales technique is used to solve the fluid-Maxwell equations in cold plasma [10, 11, 12, 13, 14].
The nonlinear Schrödinger equation (NLS) that describes the propagation of high intensity laser pulse through plasma is obtained by employing the multiple scales technique.
We summarize the strengths and limitations of currently available multiple-scale techniques, where the emphasis is made on the latest perspective approaches, such as the bridging scale method, multi-scale boundary conditions, and multi-scale fluidics.
Using the multiple-scale technique, an NLS equation is derived which governs the evolution of DIA wave envelopes.
The theoretical results are obtained to second order approximations applying the multiple scale perturbation technique (MSPT).
To accomplish this task, we first use an extension of the generalized averaging method to approximate these solutions and then apply the technique of multiple scaling to perform the stability analysis.
We discuss the appropriate strategies for sampling lacustrine sediment cores to assess the biogeochemical outcomes of disturbances and provide a review of the appropriate data scaling techniques for analyzing multiple records in space and time.
The analysis uses a multiple time-scale technique to identify three transport coefficients which characterize the interplays between convection, diffusion and surface-interactions.
Using multiple-scale analytical techniques, we report the influence of carbon addition and strain rates on the mechanical properties and associated deformation-induced phase transformation of these steels.
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