کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4610249 1338553 2014 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fourth order evolution equations which describe pseudospherical surfaces
ترجمه فارسی عنوان
معادلات تکاملی مرتبه چهارم که سطوح شبه فضایی را توصیف می کنند
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

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. They can also be described as the compatibility condition of an associated linear problem also referred to as a zero curvature representation. A complete and explicit classification of a class of fourth order evolution equations is given. The classification provides four huge classes (referred to as Types I–IV) of fourth order evolution equations that describe pseudospherical surfaces, together with the associated one (or more) parameter linear problems. The differential equations of each type are determined by choosing certain arbitrary differentiable functions. Fourth-order member of the Burgers hierarchy and a modified Kuramoto–Sivashinsky equation are examples of equations described by Types I and IV, respectively. Many other explicit examples are presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 257, Issue 9, 1 November 2014, Pages 3165–3199
نویسندگان
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