Burgers Equation – Quirky Quintet

For conservation laws in general, there’s the implicit solution of $u <p>For example, in Python it would be literally one line:</p> <pre>return optimize.fsolve(lambda u: u - self.u0(x - u*t), 1)</pre> </div> <footer class="entry-footer"><span class="cat-tags-links"><span class="cat-links"><svg class="icon icon-folder-open" aria-hidden="true" role="img"> <use href="#icon-folder-open" xlink:href="#icon-folder-open"></use> </svg><span class="screen-reader-text">Categories</span><a href="https://marshalljiang.com/category/math/" rel="category tag">Math/Programming</a></span></span></footer>  </article> <div id="comments" class="comments-area"> <div id="respond" class="comment-respond"> <h3 id="reply-title" class="comment-reply-title">Leave a Reply <small><a rel="nofollow" id="cancel-comment-reply-link" href="/burgers-equation/#respond" style="display:none;">Cancel reply</a></small></h3><form action="https://marshalljiang.com/wp-comments-post.php" method="post" id="commentform" class="comment-form" novalidate><p class="comment-notes"><span id="email-notes">Your email address will not be published.</span> <span class="required-field-message">Required fields are marked <span class="required">*</span></span></p><p class="comment-form-comment"><label for="comment">Comment <span class="required">*</span></label> <textarea id="comment" name="comment" cols="45" rows="8" maxlength="65525" required></textarea></p><p class="comment-form-author"><label for="author">Name <span class="required">*</span></label> <input id="author" name="author" type="text" value="" size="30" maxlength="245" autocomplete="name" required /></p> <p class="comment-form-email"><label for="email">Email <span class="required">*</span></label> <input id="email" name="email" type="email" value="" size="30" maxlength="100" aria-describedby="email-notes" autocomplete="email" required /></p> <p class="comment-form-url"><label for="url">Website</label> <input id="url" name="url" type="url" value="" size="30" maxlength="200" autocomplete="url" /></p> <p class="form-submit"><input name="submit" type="submit" id="submit" class="submit" value="Post Comment" /> <input type=$