Classification of Self Similar Solutions to a Generalized Burgers Equation
نویسندگان
چکیده
منابع مشابه
Self-similar solutions to a coagulation equation
The existence of self-similar solutions with a finite first moment is established for the Oort-Hulst-Safronov coagulation equation when the coagulation kernel is given by a(y, y∗) = yλ + yλ ∗ for some λ ∈ (0, 1). The corresponding self-similar profiles are compactly supported and have a discontinuity at the edge of their support. MSC 2000: 45K05, 45M05, 82C21
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Existence of self-similar solutions to the Oort-Hulst-Safronov coagulation equation with multiplicative coagulation kernel is established. These solutions are given by s(t)−τ ψτ (y/s(t)) for (t, y) ∈ (0, T )×(0,∞), where T is some arbitrary positive real number, s(t) = ((3−τ)(T − t))−1/(3−τ) and the parameter τ ranges in a given interval [τc, 3). In addition, the second moment of these self-sim...
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Exact chirped self-similar solutions of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, gain or absorption, and nonlinear gain have been found. The stability of these nonlinearly chirped solutions is then demonstrated numerically by adding Gaussian white noise and by evolving from an initial chirped Gaussian pulse, respectively. It is reported that the puls...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1208