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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.
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This suggestion, using multiple scaling techniques, points to an important issue.
Using the multiple-scale technique, an NLS equation is derived which governs the evolution of DIA wave envelopes.
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.
The theoretical results are obtained to second order approximations applying the multiple scale perturbation technique (MSPT).
Approximate analytical solutions are sought using the method of Multiple Scales, a perturbation technique.
Approximate solutions of the equations are obtained by using the method of multiple scales, a perturbation technique.
Equations of motion are solved in their general form using the method of multiple scales, a perturbation technique.
An approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.
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