One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation

We apply the Lie theory to determine the infinitesimal generators of the one-parameter point transformations which leave invariant the 3 + 1 Kudryashov–Sinelshchikov equation. We solve the classification problem of the one-dimensional optimal system, while we derive all the possible independent Lie invariants; that is, we determine all the independent similarity transformations which lead to different reductions. For an application, the results are applied to prove the existence of travel-wave solutions. Furthermore, the method of singularity analysis is applied where we show that the 3 + 1 Kudryashov–Sinelshchikov equation possess the Painlevé property and its solution can be written by using a Laurent expansion.

Characterization of Flood Waves by Rating Curves

The flood waves are characterized within the frame-work of loop (or hysteresis) of rating curves. The National Weather Service's Dam Break Flood Forecasting Model is used to generate the flood waves in the downstream valley of the Bargi dam located in Central India. The quantified hystereses, η, of non-dimensional rating curves are related with the corresponding flood wave characteristics, viz., speed of travel, wave number, phase difference, and attenuation. The analysis has led to the development of an exact relationship between η and phase difference. Using the concept of wave zoning, the better performance of the hysteresis based criteria compared with the available criteria is verified using Convex and Muskingum-Cunge routing in the wave zones. η limits are specified for the applicability of these simplified routing models. Furthermore, the envisaged applications of the based analysis are introduced.