کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609542 1338517 2016 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Second order evolution equations which describe pseudospherical surfaces
ترجمه فارسی عنوان
معادلات تکاملی مرتبه دوم که سطوح شبه فضایی را توصیف می کنند
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

Second order evolution differential equations that describe pseudospherical surfaces are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature K=−1K=−1, and can be seen as the compatibility condition of an associated sl(2,R)sl(2,R)-valued linear problem, also referred to as a zero curvature representation. Under the assumption that the linear problem is defined by 1-forms ωi=fi1dx+fi2dtωi=fi1dx+fi2dt, i=1,2,3i=1,2,3, with fijfij depending on (x,t,z,z1,z2)(x,t,z,z1,z2) and such that f21=ηf21=η, η∈Rη∈R, we give a complete and explicit classification of equations of the form zt=A(x,t,z)z2+B(x,t,z,z1)zt=A(x,t,z)z2+B(x,t,z,z1). According to the classification, these equations are subdivided in three main classes (referred to as Types I–III) together with the corresponding linear problems. Explicit examples of differential equations of each type are determined by choosing certain arbitrary differentiable functions. Svinolupov–Sokolov equations admitting higher weakly nonlinear symmetries, Boltzmann equation and reaction–diffusion equations like Murray equation are some known examples of such equations. Other explicit examples are presented, as well.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 260, Issue 11, 5 June 2016, Pages 8072–8108
نویسندگان
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