کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
759266 896471 2012 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A KdV-like advection–dispersion equation with some remarkable properties
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
A KdV-like advection–dispersion equation with some remarkable properties
چکیده انگلیسی

We discuss a new non-linear PDE, ut+(2uxx/u)ux=ϵuxxxut+(2uxx/u)ux=ϵuxxx, invariant under scaling of dependent variable and referred to here as SIdV. It is one of the simplest such translation and space–time reflection-symmetric first order advection–dispersion equations. This PDE (with dispersion coefficient unity) was discovered in a genetic programming search for equations sharing the KdV solitary wave solution. It provides a bridge between non-linear advection, diffusion and dispersion. Special cases include the mKdV and linear dispersive equations. We identify two conservation laws, though initial investigations indicate that SIdV does not follow from a polynomial Lagrangian of the KdV sort. Nevertheless, it possesses solitary and periodic travelling waves. Moreover, numerical simulations reveal recurrence properties usually associated with integrable systems. KdV and SIdV are the simplest in an infinite dimensional family of equations sharing the KdV solitary wave. SIdV and its generalizations may serve as a testing ground for numerical and analytical techniques and be a rich source for further explorations.


► New non-linear PDE sharing KdV solitary waves discovered by genetic programming.
► Simplest parity, scale-invariant advection dispersion PDE, has 2 conservation laws.
► Admits solitary, plane, periodic waves, scaling solutions but no simple Lagrangian.
► Leads to non-linear diffusion, mKdV, linear KdV at critical dispersion coefficients.
► Numerical evolution indicates recurrent behaviour without soliton scattering.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 17, Issue 11, November 2012, Pages 4115–4124
نویسندگان
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