Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

<div>Profiles of <svg height="11.6425pt" id="M89" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 13.1859 11.6425" width="13.1859pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 394 180L457 426L452 432L377 416L315 156C302 100 259 45 216 45C176 45 148 67 148 122C148 133 152 158 156 180C162 212 173 259 194 332C201 357 206 384 206 405C206 430 198 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C126 383 128 382 128 377C128 370 127 359 122 343C99 268 84 204 77 156C74 137 70 111 70 104C70 25 125 -12 180 -12C228 -12 276 12 319 50C338 8 378 -12 418 -12C549 -12 689 166 689 332Z" id="g113-120"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="712" vert-adv-y="712"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.257,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="361" vert-adv-y="361"></glyph.data></g></svg> generated by applying Bäcklund transformation (<a href="https://static.hindawi.com/articles/mpe/volume-2017/5157123/figures/#EEq24">23</a>) to rational solution (<a href="https://static.hindawi.com/articles/mpe/volume-2017/5157123/figures/#EEq18">17</a>).</div>

Mathematical Problems in Engineering

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Figure 6

Figure 6: Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation 